LMFDB - Embedded newform 547.2.m.a.10.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(10,547)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(182))

chi = DirichletCharacter(H, H._module([60]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("547.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.m (of order $91$, degree $72$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$44$ over $\Q(\zeta_{91})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{91}]$

Embedding invariants

Embedding label			10.9
Character	$\chi$	$=$	547.10
Dual form			547.2.m.a.383.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.929069 - 1.56726i) q^{2} +(-0.617025 - 2.70336i) q^{3} +(-0.633268 + 1.15758i) q^{4} +(-0.691646 - 0.0238872i) q^{5} +(-3.66362 + 3.47865i) q^{6} +(-4.21969 + 0.586437i) q^{7} +(-1.23913 + 0.0427955i) q^{8} +(-4.22454 + 2.03443i) q^{9} +O(q^{10})$	\(q+(-0.929069 - 1.56726i) q^{2} +(-0.617025 - 2.70336i) q^{3} +(-0.633268 + 1.15758i) q^{4} +(-0.691646 - 0.0238872i) q^{5} +(-3.66362 + 3.47865i) q^{6} +(-4.21969 + 0.586437i) q^{7} +(-1.23913 + 0.0427955i) q^{8} +(-4.22454 + 2.03443i) q^{9} +(0.605149 + 1.10618i) q^{10} +(3.33315 + 0.821546i) q^{11} +(3.52011 + 0.997695i) q^{12} +(-1.35182 - 1.69513i) q^{13} +(4.83948 + 6.06851i) q^{14} +(0.362187 + 1.88451i) q^{15} +(2.64155 + 4.12455i) q^{16} +(4.17462 - 3.44869i) q^{17} +(7.11337 + 4.73084i) q^{18} +(0.782372 - 0.482229i) q^{19} +(0.465649 - 0.785512i) q^{20} +(4.18900 + 11.0455i) q^{21} +(-1.80914 - 5.98719i) q^{22} +(0.365442 - 1.20940i) q^{23} +(0.880265 + 3.32341i) q^{24} +(-4.51028 - 0.311913i) q^{25} +(-1.40078 + 3.69356i) q^{26} +(2.91985 + 3.66138i) q^{27} +(1.99334 - 5.25601i) q^{28} +(-9.12227 + 5.19699i) q^{29} +(2.61702 - 2.31848i) q^{30} +(6.29734 - 2.26473i) q^{31} +(2.89575 - 5.75674i) q^{32} +(0.164305 - 9.51761i) q^{33} +(-9.28351 - 3.33865i) q^{34} +(2.93254 - 0.304811i) q^{35} +(0.320242 - 6.17860i) q^{36} +(0.0441166 - 0.281687i) q^{37} +(-1.48266 - 0.778159i) q^{38} +(-3.74845 + 4.70041i) q^{39} +0.858061 q^{40} -5.40341 q^{41} +(13.4193 - 16.8273i) q^{42} +(-2.85143 + 2.04176i) q^{43} +(-3.06178 + 3.33814i) q^{44} +(2.97048 - 1.30619i) q^{45} +(-2.23496 + 0.550869i) q^{46} +(-5.02148 + 7.27486i) q^{47} +(9.52025 - 9.68602i) q^{48} +(10.7271 - 3.04036i) q^{49} +(3.70151 + 7.35859i) q^{50} +(-11.8989 - 9.15757i) q^{51} +(2.81833 - 0.491375i) q^{52} +(2.01085 + 10.4627i) q^{53} +(3.02560 - 7.97785i) q^{54} +(-2.28573 - 0.647839i) q^{55} +(5.20364 - 0.907255i) q^{56} +(-1.78638 - 1.81749i) q^{57} +(16.6203 + 9.46863i) q^{58} +(-1.22110 - 10.0566i) q^{59} +(-2.41084 - 0.774138i) q^{60} +(-0.179947 - 2.07977i) q^{61} +(-9.40008 - 7.76549i) q^{62} +(16.6332 - 11.0621i) q^{63} +(-1.94015 + 0.134173i) q^{64} +(0.894492 + 1.20472i) q^{65} +(-15.0692 + 8.58501i) q^{66} +(7.19313 + 2.03873i) q^{67} +(1.34850 + 7.01642i) q^{68} +(-3.49493 - 0.241695i) q^{69} +(-3.20225 - 4.31287i) q^{70} +(4.98004 + 14.6361i) q^{71} +(5.14768 - 2.70171i) q^{72} +(1.87808 - 9.77191i) q^{73} +(-0.482466 + 0.192565i) q^{74} +(1.93974 + 12.3854i) q^{75} +(0.0627693 + 1.21104i) q^{76} +(-14.5466 - 1.51199i) q^{77} +(10.8493 + 1.50780i) q^{78} +(-1.86793 + 1.33752i) q^{79} +(-1.72850 - 2.91583i) q^{80} +(-0.674005 + 0.845176i) q^{81} +(5.02014 + 8.46857i) q^{82} +(-8.51542 - 4.46924i) q^{83} +(-15.4388 - 2.14564i) q^{84} +(-2.96974 + 2.28555i) q^{85} +(5.84914 + 2.57201i) q^{86} +(19.6780 + 21.4541i) q^{87} +(-4.16536 - 0.875359i) q^{88} +(-0.941816 + 10.8852i) q^{89} +(-4.80693 - 3.44198i) q^{90} +(6.69836 + 6.36017i) q^{91} +(1.16856 + 1.18890i) q^{92} +(-10.0080 - 15.6266i) q^{93} +(16.0669 + 1.11112i) q^{94} +(-0.552644 + 0.314843i) q^{95} +(-17.3493 - 4.27622i) q^{96} +(-5.95476 - 4.58287i) q^{97} +(-14.7313 - 13.9875i) q^{98} +(-15.7524 + 3.31040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) $ 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{30}{91}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.929069	−	1.56726i	−0.656951	−	1.10822i	−0.986449	−	0.164066i	$-0.947539\pi$
$2$	−0.929069	−	1.56726i	−0.656951	−	1.10822i	0.329499	−	0.944156i	$-0.393120\pi$
$3$	−0.617025	−	2.70336i	−0.356239	−	1.56079i	−0.762475	−	0.647018i	$-0.776016\pi$
$3$	−0.617025	−	2.70336i	−0.356239	−	1.56079i	0.406235	−	0.913769i	$-0.366841\pi$
$4$	−0.633268	+	1.15758i	−0.316634	+	0.578792i
$5$	−0.691646	−	0.0238872i	−0.309314	−	0.0106827i	−0.120556	−	0.992706i	$-0.538468\pi$
$5$	−0.691646	−	0.0238872i	−0.309314	−	0.0106827i	−0.188757	+	0.982024i	$0.560446\pi$
$6$	−3.66362	+	3.47865i	−1.49567	+	1.42015i
$7$	−4.21969	+	0.586437i	−1.59489	+	0.221652i	−0.879091	−	0.476653i	$-0.841850\pi$
$7$	−4.21969	+	0.586437i	−1.59489	+	0.221652i	−0.715800	+	0.698306i	$0.753938\pi$
$8$	−1.23913	+	0.0427955i	−0.438098	+	0.0151305i
$9$	−4.22454	+	2.03443i	−1.40818	+	0.678143i
$10$	0.605149	+	1.10618i	0.191365	+	0.349806i
$11$	3.33315	+	0.821546i	1.00498	+	0.247706i	0.707265	−	0.706949i	$-0.249929\pi$
$11$	3.33315	+	0.821546i	1.00498	+	0.247706i	0.297716	+	0.954654i	$0.403775\pi$
$12$	3.52011	+	0.997695i	1.01617	+	0.288010i
$13$	−1.35182	−	1.69513i	−0.374928	−	0.470145i	0.558191	−	0.829713i	$-0.311496\pi$
$13$	−1.35182	−	1.69513i	−0.374928	−	0.470145i	−0.933119	+	0.359567i	$0.882924\pi$
$14$	4.83948	+	6.06851i	1.29341	+	1.62188i
$15$	0.362187	+	1.88451i	0.0935163	+	0.486578i
$16$	2.64155	+	4.12455i	0.660388	+	1.03114i
$17$	4.17462	−	3.44869i	1.01249	−	0.836430i	0.0259057	−	0.999664i	$-0.491753\pi$
$17$	4.17462	−	3.44869i	1.01249	−	0.836430i	0.986587	+	0.163234i	$0.0521926\pi$
$18$	7.11337	+	4.73084i	1.67664	+	1.11507i
$19$	0.782372	−	0.482229i	0.179488	−	0.110631i	−0.432036	−	0.901856i	$-0.642205\pi$
$19$	0.782372	−	0.482229i	0.179488	−	0.110631i	0.611525	+	0.791225i	$0.290556\pi$
$20$	0.465649	−	0.785512i	0.104122	−	0.175646i
$21$	4.18900	+	11.0455i	0.914115	+	2.41032i
$22$	−1.80914	−	5.98719i	−0.385710	−	1.27647i
$23$	0.365442	−	1.20940i	0.0762000	−	0.252177i	−0.910812	−	0.412820i	$-0.864544\pi$
$23$	0.365442	−	1.20940i	0.0762000	−	0.252177i	0.987012	+	0.160643i	$0.0513569\pi$
$24$	0.880265	+	3.32341i	0.179683	+	0.678388i
$25$	−4.51028	−	0.311913i	−0.902057	−	0.0623826i
$26$	−1.40078	+	3.69356i	−0.274716	+	0.724366i
$27$	2.91985	+	3.66138i	0.561926	+	0.704633i
$28$	1.99334	−	5.25601i	0.376706	−	0.993293i
$29$	−9.12227	+	5.19699i	−1.69396	+	0.965057i	−0.736529	+	0.676405i	$0.763537\pi$
$29$	−9.12227	+	5.19699i	−1.69396	+	0.965057i	−0.957434	+	0.288652i	$0.906793\pi$
$30$	2.61702	−	2.31848i	0.477801	−	0.423295i
$31$	6.29734	−	2.26473i	1.13104	−	0.406757i	0.295035	−	0.955486i	$-0.404669\pi$
$31$	6.29734	−	2.26473i	1.13104	−	0.406757i	0.836000	+	0.548730i	$0.184888\pi$
$32$	2.89575	−	5.75674i	0.511902	−	1.01766i
$33$	0.164305	−	9.51761i	0.0286018	−	1.65680i
$34$	−9.28351	−	3.33865i	−1.59211	−	0.572574i
$35$	2.93254	−	0.304811i	0.495689	−	0.0515224i
$36$	0.320242	−	6.17860i	0.0533737	−	1.02977i
$37$	0.0441166	−	0.281687i	0.00725273	−	0.0463091i	−0.984059	−	0.177841i	$-0.943089\pi$
$37$	0.0441166	−	0.281687i	0.00725273	−	0.0463091i	0.991312	+	0.131532i	$0.0419897\pi$
$38$	−1.48266	−	0.778159i	−0.240519	−	0.126234i
$39$	−3.74845	+	4.70041i	−0.600232	+	0.752668i
$40$	0.858061			0.135671
$41$	−5.40341			−0.843871			−0.421936	−	0.906626i	$-0.638649\pi$
$41$	−5.40341			−0.843871			−0.421936	+	0.906626i	$0.638649\pi$
$42$	13.4193	−	16.8273i	2.07064	−	2.59651i
$43$	−2.85143	+	2.04176i	−0.434839	+	0.311365i	−0.778403	−	0.627764i	$-0.783970\pi$
$43$	−2.85143	+	2.04176i	−0.434839	+	0.311365i	0.343564	+	0.939129i	$0.388366\pi$
$44$	−3.06178	+	3.33814i	−0.461581	+	0.503243i
$45$	2.97048	−	1.30619i	0.442813	−	0.194716i
$46$	−2.23496	+	0.550869i	−0.329528	+	0.0812212i
$47$	−5.02148	+	7.27486i	−0.732458	+	1.06115i	0.262892	+	0.964825i	$0.415324\pi$
$47$	−5.02148	+	7.27486i	−0.732458	+	1.06115i	−0.995350	+	0.0963230i	$0.969292\pi$
$48$	9.52025	−	9.68602i	1.37413	−	1.39806i
$49$	10.7271	−	3.04036i	1.53244	−	0.434337i
$50$	3.70151	+	7.35859i	0.523473	+	1.04066i
$51$	−11.8989	−	9.15757i	−1.66618	−	1.28232i
$52$	2.81833	−	0.491375i	0.390832	−	0.0681415i
$53$	2.01085	+	10.4627i	0.276211	+	1.43717i	0.807446	+	0.589941i	$0.200849\pi$
$53$	2.01085	+	10.4627i	0.276211	+	1.43717i	−0.531235	+	0.847224i	$0.678272\pi$
$54$	3.02560	−	7.97785i	0.411732	−	1.08565i
$55$	−2.28573	−	0.647839i	−0.308208	−	0.0873546i
$56$	5.20364	−	0.907255i	0.695365	−	0.121237i
$57$	−1.78638	−	1.81749i	−0.236612	−	0.240732i
$58$	16.6203	+	9.46863i	2.18235	+	1.24329i
$59$	−1.22110	−	10.0566i	−0.158973	−	1.30926i	−0.825764	−	0.564016i	$-0.809256\pi$
$59$	−1.22110	−	10.0566i	−0.158973	−	1.30926i	0.666791	−	0.745245i	$-0.267667\pi$
$60$	−2.41084	−	0.774138i	−0.311238	−	0.0999407i
$61$	−0.179947	−	2.07977i	−0.0230398	−	0.266287i	−0.998861	−	0.0477165i	$-0.984806\pi$
$61$	−0.179947	−	2.07977i	−0.0230398	−	0.266287i	0.975821	−	0.218571i	$-0.0701395\pi$
$62$	−9.40008	−	7.76549i	−1.19381	−	0.986219i
$63$	16.6332	−	11.0621i	2.09558	−	1.39369i
$64$	−1.94015	+	0.134173i	−0.242519	+	0.0167716i
$65$	0.894492	+	1.20472i	0.110948	+	0.149428i
$66$	−15.0692	+	8.58501i	−1.85490	+	1.05674i
$67$	7.19313	+	2.03873i	0.878780	+	0.249070i	0.681978	−	0.731373i	$-0.261120\pi$
$67$	7.19313	+	2.03873i	0.878780	+	0.249070i	0.196803	+	0.980443i	$0.436944\pi$
$68$	1.34850	+	7.01642i	0.163529	+	0.850865i
$69$	−3.49493	−	0.241695i	−0.420740	−	0.0290966i
$70$	−3.20225	−	4.31287i	−0.382742	−	0.515486i
$71$	4.98004	+	14.6361i	0.591022	+	1.73699i	0.672282	+	0.740296i	$0.265314\pi$
$71$	4.98004	+	14.6361i	0.591022	+	1.73699i	−0.0812598	+	0.996693i	$0.525894\pi$
$72$	5.14768	−	2.70171i	0.606660	−	0.318400i
$73$	1.87808	−	9.77191i	0.219813	−	1.14372i	−0.688440	−	0.725293i	$-0.741704\pi$
$73$	1.87808	−	9.77191i	0.219813	−	1.14372i	0.908253	−	0.418422i	$-0.137417\pi$
$74$	−0.482466	+	0.192565i	−0.0560855	+	0.0223852i
$75$	1.93974	+	12.3854i	0.223982	+	1.43014i
$76$	0.0627693	+	1.21104i	0.00720013	+	0.138916i
$77$	−14.5466	−	1.51199i	−1.65774	−	0.172307i
$78$	10.8493	+	1.50780i	1.22845	+	0.170725i
$79$	−1.86793	+	1.33752i	−0.210158	+	0.150483i	−0.682382	−	0.730996i	$-0.739056\pi$
$79$	−1.86793	+	1.33752i	−0.210158	+	0.150483i	0.472224	+	0.881479i	$0.343452\pi$
$80$	−1.72850	−	2.91583i	−0.193252	−	0.326000i
$81$	−0.674005	+	0.845176i	−0.0748895	+	0.0939084i
$82$	5.02014	+	8.46857i	0.554382	+	0.935197i
$83$	−8.51542	−	4.46924i	−0.934689	−	0.490563i	−0.0726236	−	0.997359i	$-0.523137\pi$
$83$	−8.51542	−	4.46924i	−0.934689	−	0.490563i	−0.862066	+	0.506797i	$0.830829\pi$
$84$	−15.4388	−	2.14564i	−1.68452	−	0.234108i
$85$	−2.96974	+	2.28555i	−0.322113	+	0.247903i
$86$	5.84914	+	2.57201i	0.630729	+	0.277347i
$87$	19.6780	+	21.4541i	2.10971	+	2.30012i
$88$	−4.16536	−	0.875359i	−0.444028	−	0.0933136i
$89$	−0.941816	+	10.8852i	−0.0998323	+	1.15383i	0.762326	+	0.647193i	$0.224057\pi$
$89$	−0.941816	+	10.8852i	−0.0998323	+	1.15383i	−0.862159	+	0.506639i	$0.830888\pi$
$90$	−4.80693	−	3.44198i	−0.506695	−	0.362817i
$91$	6.69836	+	6.36017i	0.702179	+	0.666727i
$92$	1.16856	+	1.18890i	0.121830	+	0.123952i
$93$	−10.0080	−	15.6266i	−1.03778	−	1.62040i
$94$	16.0669	+	1.11112i	1.65718	+	0.114604i
$95$	−0.552644	+	0.314843i	−0.0567001	+	0.0323022i
$96$	−17.3493	−	4.27622i	−1.77071	−	0.436440i
$97$	−5.95476	−	4.58287i	−0.604614	−	0.465320i	0.261475	−	0.965210i	$-0.415791\pi$
$97$	−5.95476	−	4.58287i	−0.604614	−	0.465320i	−0.866089	+	0.499890i	$0.833374\pi$
$98$	−14.7313	−	13.9875i	−1.48808	−	1.41295i
$99$	−15.7524	+	3.31040i	−1.58317	+	0.332707i
$100$	3.21728	−	5.02351i	0.321728	−	0.502351i
$101$	−3.65535	+	4.92311i	−0.363721	+	0.489868i	−0.946474	−	0.322781i	$-0.895382\pi$
$101$	−3.65535	+	4.92311i	−0.363721	+	0.489868i	0.582753	+	0.812649i	$0.301976\pi$
$102$	−3.29742	+	27.1567i	−0.326493	+	2.68891i
$103$	0.666849	−	1.44815i	0.0657066	−	0.142691i	−0.872664	−	0.488321i	$-0.837610\pi$
$103$	0.666849	−	1.44815i	0.0657066	−	0.142691i	0.938371	+	0.345630i	$0.112335\pi$
$104$	1.74763	+	2.04264i	0.171369	+	0.200297i
$105$	−2.63346	−	7.73963i	−0.256999	−	0.755311i
$106$	14.5296	−	12.8721i	1.41124	−	1.25025i
$107$	−0.810274	−	0.199715i	−0.0783322	−	0.0193071i	0.199955	−	0.979805i	$-0.435920\pi$
$107$	−0.810274	−	0.199715i	−0.0783322	−	0.0193071i	−0.278287	+	0.960498i	$0.589767\pi$
$108$	−6.08740	+	1.06134i	−0.585761	+	0.102127i
$109$	−6.57689	−	10.2692i	−0.629952	−	0.983615i	−0.998540	−	0.0540217i	$-0.982796\pi$
$109$	−6.57689	−	10.2692i	−0.629952	−	0.983615i	0.368588	−	0.929593i	$-0.379841\pi$
$110$	1.10827	+	4.18423i	0.105669	+	0.398951i
$111$	−0.788724	+	0.0545449i	−0.0748624	+	0.00517718i
$112$	−13.5653	−	15.8552i	−1.28180	−	1.49818i
$113$	−15.8515	−	9.77034i	−1.49118	−	0.919116i	−0.998812	−	0.0487293i	$-0.984483\pi$
$113$	−15.8515	−	9.77034i	−1.49118	−	0.919116i	−0.492369	−	0.870387i	$-0.663869\pi$
$114$	−1.18881	+	4.48830i	−0.111342	+	0.420368i
$115$	−0.281646	+	0.827746i	−0.0262636	+	0.0771877i
$116$	−0.239111	−	13.8509i	−0.0222009	−	1.28602i
$117$	9.15946	+	4.41096i	0.846793	+	0.407794i
$118$	−14.6269	+	11.2571i	−1.34651	+	1.03630i
$119$	−15.5931	+	17.0005i	−1.42942	+	1.55844i
$120$	−0.529445	−	2.31965i	−0.0483315	−	0.211754i
$121$	0.694902	+	0.364713i	0.0631729	+	0.0331557i
$122$	−3.09236	+	2.21427i	−0.279969	+	0.200471i
$123$	3.33404	+	14.6074i	0.300620	+	1.31710i
$124$	−1.36629	+	8.72388i	−0.122697	+	0.783427i
$125$	6.55382	+	0.681210i	0.586191	+	0.0609293i
$126$	−32.7905	−	15.7911i	−2.92121	−	1.40678i
$127$	3.93895	+	0.686757i	0.349526	+	0.0609398i	0.343798	−	0.939044i	$-0.388287\pi$
$127$	3.93895	+	0.686757i	0.349526	+	0.0609398i	0.00572802	+	0.999984i	$0.498177\pi$
$128$	−5.30842	−	7.69058i	−0.469203	−	0.679758i
$129$	7.27901	+	6.44864i	0.640881	+	0.567771i
$130$	1.05707	−	2.52117i	0.0927115	−	0.221122i
$131$	0.602208	−	0.126555i	0.0526151	−	0.0110572i	−0.179278	−	0.983798i	$-0.557376\pi$
$131$	0.602208	−	0.126555i	0.0526151	−	0.0110572i	0.231893	+	0.972741i	$0.425508\pi$
$132$	10.9134	+	6.21740i	0.949888	+	0.541155i
$133$	−3.01857	+	2.49367i	−0.261743	+	0.216228i
$134$	−3.48769	−	13.1676i	−0.301290	−	1.13751i
$135$	−1.93204	−	2.60212i	−0.166284	−	0.223955i
$136$	−5.02530	+	4.45203i	−0.430916	+	0.381758i
$137$	10.4833	+	19.1629i	0.895647	+	1.63720i	0.763346	+	0.645990i	$0.223555\pi$
$137$	10.4833	+	19.1629i	0.895647	+	1.63720i	0.132301	+	0.991210i	$0.457763\pi$
$138$	2.86823	+	5.70202i	0.244160	+	0.485388i
$139$	6.36861	+	4.56022i	0.540179	+	0.386793i	0.819214	−	0.573488i	$-0.194410\pi$
$139$	6.36861	+	4.56022i	0.540179	+	0.386793i	−0.279035	+	0.960281i	$0.590015\pi$
$140$	−1.50424	+	3.58769i	−0.127131	+	0.303215i
$141$	22.7650	+	9.08610i	1.91716	+	0.765187i
$142$	18.3119	−	21.4030i	1.53670	−	1.79610i
$143$	−3.11319	−	6.76071i	−0.260338	−	0.565359i
$144$	−19.5505	−	12.0503i	−1.62920	−	1.00419i
$145$	6.43353	−	3.37657i	0.534275	−	0.280409i
$146$	−17.0600	+	6.13533i	−1.41190	+	0.507763i
$147$	−14.8381	−	27.1233i	−1.22382	−	2.23709i
$148$	0.298139	+	0.229452i	0.0245069	+	0.0188609i
$149$	−3.73635	−	3.80141i	−0.306094	−	0.311423i	0.542930	−	0.839778i	$-0.317315\pi$
$149$	−3.73635	−	3.80141i	−0.306094	−	0.311423i	−0.849024	+	0.528354i	$0.822809\pi$
$150$	17.6090	−	14.5470i	1.43777	−	1.18775i
$151$	3.26227	−	10.7962i	0.265480	−	0.878580i	−0.717764	−	0.696286i	$-0.754835\pi$
$151$	3.26227	−	10.7962i	0.265480	−	0.878580i	0.983244	−	0.182294i	$-0.0583523\pi$
$152$	−0.948823	+	0.631026i	−0.0769597	+	0.0511830i
$153$	−10.6197	+	23.0621i	−0.858552	+	1.86446i
$154$	11.1451	+	24.2031i	0.898099	+	1.95034i
$155$	−4.40963	+	1.41596i	−0.354190	+	0.113733i
$156$	−3.06734	−	7.31577i	−0.245584	−	0.585730i
$157$	−19.9672	−	3.48129i	−1.59356	−	0.277837i	−0.695771	−	0.718264i	$-0.744937\pi$
$157$	−19.9672	−	3.48129i	−1.59356	−	0.277837i	−0.897788	+	0.440427i	$0.854827\pi$
$158$	3.83168	+	1.68489i	0.304832	+	0.134042i
$159$	27.0438	−	11.8918i	2.14471	−	0.943082i
$160$	−2.14035	+	3.91245i	−0.169209	+	0.309307i
$161$	−0.832816	+	5.31759i	−0.0656351	+	0.419084i
$162$	1.95081	+	0.271117i	0.153270	+	0.0213009i
$163$	−10.1057	+	11.0178i	−0.791541	+	0.862984i	−0.993194	−	0.116473i	$-0.962841\pi$
$163$	−10.1057	+	11.0178i	−0.791541	+	0.862984i	0.201653	+	0.979457i	$0.435369\pi$
$164$	3.42181	−	6.25491i	0.267199	−	0.488426i
$165$	−0.340990	+	6.57889i	−0.0265460	+	0.512166i
$166$	0.906943	+	17.4981i	0.0703924	+	1.35812i
$167$	0.206786	+	11.9784i	0.0160016	+	0.926919i	0.893951	+	0.448165i	$0.147922\pi$
$167$	0.206786	+	11.9784i	0.0160016	+	0.926919i	−0.877949	+	0.478754i	$0.841089\pi$
$168$	−5.66341	−	13.5075i	−0.436942	−	1.04213i
$169$	1.84672	−	8.09102i	0.142056	−	0.622386i
$170$	6.34115	+	2.53092i	0.486344	+	0.194113i
$171$	−2.32410	+	3.62888i	−0.177728	+	0.277507i
$172$	−0.557782	−	4.59375i	−0.0425305	−	0.350270i
$173$	5.85824	+	3.89609i	0.445394	+	0.296215i	0.756299	−	0.654226i	$-0.227006\pi$
$173$	5.85824	+	3.89609i	0.445394	+	0.296215i	−0.310905	+	0.950441i	$0.600632\pi$
$174$	15.3420	−	50.7730i	1.16308	−	3.84909i
$175$	19.2149	−	1.32882i	1.45251	−	0.100450i
$176$	5.41617	+	15.9179i	0.408259	+	1.19986i
$177$	−26.4332	+	9.50625i	−1.98684	+	0.714533i
$178$	17.9350	−	8.63705i	1.34429	−	0.647374i
$179$	−11.7858	+	3.34041i	−0.880909	+	0.249674i	−0.682887	−	0.730524i	$-0.739276\pi$
$179$	−11.7858	+	3.34041i	−0.880909	+	0.249674i	−0.198022	+	0.980198i	$0.563452\pi$
$180$	−0.369083	+	4.26575i	−0.0275099	+	0.317951i
$181$	−13.1813	−	11.6776i	−0.979760	−	0.867992i	0.0114971	−	0.999934i	$-0.496340\pi$
$181$	−13.1813	−	11.6776i	−0.979760	−	0.867992i	−0.991257	+	0.131942i	$0.957879\pi$
$182$	3.74482	−	16.4071i	0.277584	−	1.21618i
$183$	−5.51134	+	1.76973i	−0.407410	+	0.130822i
$184$	−0.401074	+	1.51424i	−0.0295675	+	0.111631i
$185$	−0.0372418	+	0.193774i	−0.00273807	+	0.0142466i
$186$	−15.1929	+	30.2033i	−1.11399	+	2.21461i
$187$	16.7479	−	8.06534i	1.22472	−	0.589796i
$188$	−5.24133	−	10.4197i	−0.382263	−	0.759936i
$189$	−14.4680	−	13.7376i	−1.05239	−	0.999260i
$190$	1.00689	+	0.573627i	0.0730472	+	0.0416153i
$191$	9.16080	+	6.09250i	0.662852	+	0.440838i	0.839444	−	0.543446i	$-0.182881\pi$
$191$	9.16080	+	6.09250i	0.662852	+	0.440838i	−0.176592	+	0.984284i	$0.556507\pi$
$192$	1.55984	+	5.16215i	0.112572	+	0.372546i
$193$	−8.96717	−	7.40787i	−0.645471	−	0.533230i	0.255665	−	0.966765i	$-0.417705\pi$
$193$	−8.96717	−	7.40787i	−0.645471	−	0.533230i	−0.901137	+	0.433535i	$0.857266\pi$
$194$	−1.65018	+	13.5905i	−0.118476	+	0.975739i
$195$	2.70488	−	3.16148i	0.193700	−	0.226398i
$196$	−3.27367	+	14.3429i	−0.233834	+	1.02449i
$197$	−8.73926	−	12.6610i	−0.622646	−	0.902059i	0.377063	−	0.926188i	$-0.376934\pi$
$197$	−8.73926	−	12.6610i	−0.622646	−	0.902059i	−0.999709	+	0.0241289i	$0.992319\pi$
$198$	19.8233	+	21.6125i	1.40878	+	1.53594i
$199$	−18.2909	+	4.50829i	−1.29660	+	0.319584i	−0.826455	−	0.563002i	$-0.809646\pi$
$199$	−18.2909	+	4.50829i	−1.29660	+	0.319584i	−0.470149	+	0.882587i	$0.655800\pi$
$200$	5.60217	+	0.193481i	0.396133	+	0.0136811i
$201$	1.07308	−	20.7036i	0.0756895	−	1.46032i
$202$	11.1119	+	1.15498i	0.781829	+	0.0812640i
$203$	35.4454	−	27.2793i	2.48778	−	1.91463i
$204$	18.1359	−	7.97478i	1.26976	−	0.558346i
$205$	3.73725	+	0.129072i	0.261021	+	0.00901480i
$206$	−2.88918	+	0.300304i	−0.201299	+	0.0209232i
$207$	0.916610	+	5.85261i	0.0637088	+	0.406785i
$208$	3.42075	−	10.0535i	0.237187	−	0.697082i
$209$	3.00393	−	0.964585i	0.207786	−	0.0667217i
$210$	−9.68337	+	11.3180i	−0.668216	+	0.781015i
$211$	6.01671	−	8.10345i	0.414207	−	0.557865i	−0.545773	−	0.837933i	$-0.683764\pi$
$211$	6.01671	−	8.10345i	0.414207	−	0.557865i	0.959980	+	0.280069i	$0.0903572\pi$
$212$	−13.3849	−	4.29798i	−0.919278	−	0.295187i
$213$	36.4939	−	22.4937i	2.50052	−	1.54124i
$214$	0.439795	+	1.45546i	0.0300638	+	0.0994933i
$215$	2.02095	−	1.34406i	0.137828	−	0.0916641i
$216$	−3.77476	−	4.41196i	−0.256840	−	0.300196i
$217$	−25.2447	+	13.2494i	−1.71372	+	0.899429i
$218$	−9.98421	+	19.8485i	−0.676216	+	1.34431i
$219$	−27.5758	+	0.952378i	−1.86340	+	0.0643558i
$220$	2.19741	−	2.23567i	0.148149	−	0.150729i
$221$	−11.4893	−	2.41451i	−0.772856	−	0.162417i
$222$	0.818265	+	1.18546i	0.0549184	+	0.0795630i
$223$	3.20297	+	7.63925i	0.214487	+	0.511562i	0.993282	−	0.115716i	$-0.0369163\pi$
$223$	3.20297	+	7.63925i	0.214487	+	0.511562i	−0.778796	+	0.627278i	$0.784169\pi$
$224$	−8.84320	+	25.9898i	−0.590861	+	1.73652i
$225$	19.6884	−	7.85817i	1.31256	−	0.523878i
$226$	−0.585581	+	33.9207i	−0.0389523	+	2.25637i
$227$	9.94608	−	0.343505i	0.660145	−	0.0227992i	0.297493	−	0.954724i	$-0.403849\pi$
$227$	9.94608	−	0.343505i	0.660145	−	0.0227992i	0.362652	+	0.931925i	$0.381871\pi$
$228$	3.23515	−	0.916931i	0.214253	−	0.0607252i
$229$	−5.54114	−	3.96771i	−0.366169	−	0.262194i	0.384149	−	0.923271i	$-0.374495\pi$
$229$	−5.54114	−	3.96771i	−0.366169	−	0.262194i	−0.750318	+	0.661078i	$0.770099\pi$
$230$	1.55896	−	0.327620i	0.102795	−	0.0216026i
$231$	4.88817	+	40.2577i	0.321618	+	2.64876i
$232$	11.0813	−	6.83014i	0.727521	−	0.448421i
$233$	−7.40651	−	19.5294i	−0.485217	−	1.27941i	−0.924541	−	0.381083i	$-0.875551\pi$
$233$	−7.40651	−	19.5294i	−0.485217	−	1.27941i	0.439324	−	0.898329i	$-0.355218\pi$
$234$	−1.59663	−	18.4534i	−0.104375	−	1.20633i
$235$	3.64686	−	4.91168i	0.237895	−	0.320403i
$236$	12.4147	+	4.95502i	0.808126	+	0.322544i
$237$	4.76837	+	4.22440i	0.309739	+	0.274405i
$238$	41.1314	+	8.64385i	2.66615	+	0.560298i
$239$	−3.34318	+	4.84343i	−0.216252	+	0.313296i	−0.916064	−	0.401032i	$-0.868652\pi$
$239$	−3.34318	+	4.84343i	−0.216252	+	0.313296i	0.699812	+	0.714327i	$0.253267\pi$
$240$	−6.81602	+	6.47189i	−0.439972	+	0.417759i
$241$	−9.21438	+	0.957751i	−0.593550	+	0.0616942i	−0.395450	−	0.918488i	$-0.629411\pi$
$241$	−9.21438	+	0.957751i	−0.593550	+	0.0616942i	−0.198100	+	0.980182i	$0.563477\pi$
$242$	−0.0740112	−	1.42794i	−0.00475762	−	0.0917913i
$243$	15.3586	+	7.39632i	0.985256	+	0.474474i
$244$	2.52146	+	1.10875i	0.161420	+	0.0709804i
$245$	−7.49199	+	1.84661i	−0.478646	+	0.117976i
$246$	19.7961	−	18.7966i	1.26215	−	1.19843i
$247$	−1.87507	−	0.674336i	−0.119308	−	0.0429070i
$248$	−7.70629	+	3.07578i	−0.489350	+	0.195312i
$249$	−6.82774	+	25.7779i	−0.432691	+	1.63361i
$250$	−5.02131	−	10.9044i	−0.317576	−	0.689658i
$251$	0.759173	−	6.25236i	0.0479186	−	0.394645i	−0.948941	−	0.315454i	$-0.897843\pi$
$251$	0.759173	−	6.25236i	0.0479186	−	0.394645i	0.996859	−	0.0791911i	$-0.0252337\pi$
$252$	2.27204	+	26.2595i	0.143125	+	1.65420i
$253$	2.21165	−	3.73087i	0.139045	−	0.234558i
$254$	−2.58323	−	6.81142i	−0.162086	−	0.427386i
$255$	8.01108	+	6.61803i	0.501673	+	0.414437i
$256$	−8.74815	+	18.9978i	−0.546759	+	1.18736i
$257$	−20.7347	−	12.7802i	−1.29340	−	0.797208i	−0.305480	−	0.952199i	$-0.598817\pi$
$257$	−20.7347	−	12.7802i	−1.29340	−	0.797208i	−0.987916	+	0.154991i	$0.950465\pi$
$258$	3.34401	−	17.3993i	0.208189	−	1.08324i
$259$	−0.0209662	+	1.21450i	−0.00130278	+	0.0754656i
$260$	−1.96102	+	0.272536i	−0.121617	+	0.0169020i
$261$	27.9645	−	40.5135i	1.73096	−	2.50772i
$262$	−0.757838	−	0.826239i	−0.0468194	−	0.0510452i
$263$	−10.9288	−	1.90544i	−0.673898	−	0.117494i	−0.175549	−	0.984471i	$-0.556170\pi$
$263$	−10.9288	−	1.90544i	−0.673898	−	0.117494i	−0.498349	+	0.866976i	$0.666060\pi$
$264$	0.203716	+	11.8006i	0.0125378	+	0.726276i
$265$	−1.14087	−	7.28453i	−0.0700831	−	0.447485i
$266$	6.71269	+	2.41410i	0.411581	+	0.148018i
$267$	30.0078	−	4.17038i	1.83645	−	0.255223i
$268$	−6.91518	+	7.03559i	−0.422412	+	0.429767i
$269$	0.197185	−	2.27901i	0.0120226	−	0.138953i	−0.987841	−	0.155467i	$-0.950312\pi$
$269$	0.197185	−	2.27901i	0.0120226	−	0.138953i	0.999864	+	0.0165138i	$0.00525674\pi$
$270$	−2.28321	+	5.44557i	−0.138952	+	0.331407i
$271$	3.14401	−	4.90909i	0.190985	−	0.298206i	−0.733303	−	0.679902i	$-0.762022\pi$
$271$	3.14401	−	4.90909i	0.190985	−	0.298206i	0.924288	+	0.381696i	$0.124660\pi$
$272$	25.2518	+	8.10853i	1.53111	+	0.491652i
$273$	13.0608	−	22.0325i	0.790475	−	1.33347i
$274$	20.2937	−	34.2337i	1.22598	−	2.06814i
$275$	−14.7772	−	4.74506i	−0.891097	−	0.286138i
$276$	2.49301	−	3.89261i	0.150061	−	0.234308i
$277$	−2.55143	+	6.08528i	−0.153300	+	0.365629i	−0.980568	−	0.196179i	$-0.937147\pi$
$277$	−2.55143	+	6.08528i	−0.153300	+	0.365629i	0.827268	+	0.561808i	$0.189894\pi$
$278$	1.23018	−	14.2180i	0.0737813	−	0.852742i
$279$	−21.9959	+	22.3789i	−1.31686	+	1.33979i
$280$	−3.62075	+	0.503199i	−0.216381	+	0.0300719i
$281$	−1.09251	−	0.392902i	−0.0651737	−	0.0234386i	0.305623	−	0.952153i	$-0.401135\pi$
$281$	−1.09251	−	0.392902i	−0.0651737	−	0.0234386i	−0.370797	+	0.928714i	$0.620915\pi$
$282$	−6.90992	−	44.1203i	−0.411480	−	2.62732i
$283$	0.221265	+	12.8172i	0.0131529	+	0.761901i	0.931011	+	0.364992i	$0.118928\pi$
$283$	0.221265	+	12.8172i	0.0131529	+	0.761901i	−0.917858	+	0.396909i	$0.870083\pi$
$284$	−20.0962	−	3.50378i	−1.19249	−	0.207911i
$285$	1.19213	+	1.29973i	0.0706157	+	0.0769894i
$286$	−7.70344	+	11.1604i	−0.455514	+	0.659926i
$287$	22.8007	−	3.16876i	1.34588	−	0.187046i
$288$	−0.521535	+	30.2108i	−0.0307317	+	1.78019i
$289$	2.32541	−	12.0994i	0.136789	−	0.711732i
$290$	−11.2692	−	6.94595i	−0.661748	−	0.407880i
$291$	−8.71493	+	18.9256i	−0.510878	+	1.10944i
$292$	10.1225	+	8.36227i	0.592373	+	0.489365i
$293$	−7.97813	−	21.0366i	−0.466087	−	1.22897i	−0.937787	−	0.347212i	$-0.887128\pi$
$293$	−7.97813	−	21.0366i	−0.466087	−	1.22897i	0.471699	−	0.881760i	$-0.343641\pi$
$294$	−28.7237	+	48.4546i	−1.67520	+	2.82593i
$295$	0.604341	+	6.98479i	0.0351861	+	0.406670i
$296$	−0.0426112	+	0.350935i	−0.00247673	+	0.0203977i
$297$	6.72430	+	14.6027i	0.390183	+	0.847334i
$298$	−2.48648	+	9.38761i	−0.144038	+	0.543809i
$299$	−2.54410	+	1.01542i	−0.147129	+	0.0587232i
$300$	−15.5655	−	5.59786i	−0.898675	−	0.323192i
$301$	10.8348	−	10.2878i	0.624507	−	0.592976i
$302$	−19.9513	+	4.91756i	−1.14807	+	0.282974i
$303$	15.5644	+	6.84405i	0.894151	+	0.393180i
$304$	4.05566	+	1.95310i	0.232608	+	0.112018i
$305$	0.0747796	+	1.44276i	0.00428187	+	0.0826124i
$306$	46.0108	−	4.78240i	2.63026	−	0.273392i
$307$	22.8677	−	21.7132i	1.30513	−	1.23924i	0.352245	−	0.935908i	$-0.385418\pi$
$307$	22.8677	−	21.7132i	1.30513	−	1.23924i	0.952886	−	0.303329i	$-0.0980980\pi$
$308$	10.9622	−	15.8814i	0.624627	−	0.904928i
$309$	−4.32634	−	0.909190i	−0.246117	−	0.0517220i
$310$	6.31603	+	5.59552i	0.358726	+	0.317804i
$311$	6.84996	+	2.73400i	0.388426	+	0.155031i	0.556709	−	0.830708i	$-0.312064\pi$
$311$	6.84996	+	2.73400i	0.388426	+	0.155031i	−0.168283	+	0.985739i	$0.553822\pi$
$312$	4.44366	−	5.98483i	0.251573	−	0.338824i
$313$	2.48931	+	28.7707i	0.140704	+	1.62621i	0.646049	+	0.763296i	$0.276420\pi$
$313$	2.48931	+	28.7707i	0.140704	+	1.62621i	−0.505345	+	0.862918i	$0.668635\pi$
$314$	13.0948	+	34.5283i	0.738985	+	1.94854i
$315$	−11.7685	+	7.25373i	−0.663080	+	0.408701i
$316$	−0.365395	−	3.00930i	−0.0205551	−	0.169286i
$317$	15.1285	−	3.17928i	0.849699	−	0.178566i	0.239581	−	0.970876i	$-0.422990\pi$
$317$	15.1285	−	3.17928i	0.849699	−	0.178566i	0.610118	+	0.792310i	$0.291122\pi$
$318$	−43.7631	−	31.3364i	−2.45411	−	1.75726i
$319$	−34.6754	+	9.82796i	−1.94145	+	0.550260i
$320$	1.34510	−	0.0464555i	0.0751936	−	0.00259694i
$321$	−0.0399418	+	2.31369i	−0.00222933	+	0.129138i
$322$	9.10780	−	3.63516i	0.507558	−	0.202580i
$323$	1.60304	−	4.71128i	0.0891958	−	0.262143i
$324$	−0.551536	−	1.31544i	−0.0306409	−	0.0730800i
$325$	5.56837	+	8.06718i	0.308878	+	0.447487i
$326$	26.6568	+	5.60198i	1.47638	+	0.310265i
$327$	−23.7034	+	24.1161i	−1.31080	+	1.33362i
$328$	6.69553	−	0.231242i	0.369699	−	0.0127682i
$329$	16.9228	−	33.6424i	0.932984	−	1.85477i
$330$	10.6277	−	5.57782i	0.585033	−	0.307049i
$331$	−1.00078	−	1.16971i	−0.0550076	−	0.0642931i	0.731661	−	0.681669i	$-0.238745\pi$
$331$	−1.00078	−	1.16971i	−0.0550076	−	0.0642931i	−0.786669	+	0.617375i	$0.788196\pi$
$332$	10.5661	−	7.02709i	0.579888	−	0.385662i
$333$	0.386701	+	1.27975i	0.0211911	+	0.0701299i
$334$	18.5812	−	11.4529i	1.01672	−	0.626673i
$335$	−4.92640	−	1.58190i	−0.269158	−	0.0864285i
$336$	−34.4922	+	46.4550i	−1.88171	+	2.53433i
$337$	−13.4521	+	15.7229i	−0.732783	+	0.856480i	−0.994066	−	0.108782i	$-0.965305\pi$
$337$	−13.4521	+	15.7229i	−0.732783	+	0.856480i	0.261283	+	0.965262i	$0.415854\pi$
$338$	−14.3965	+	4.62281i	−0.783066	+	0.251448i
$339$	−16.6320	+	48.8808i	−0.903327	+	2.65484i
$340$	−0.765080	−	4.88509i	−0.0414923	−	0.264931i
$341$	22.8505	−	2.37510i	1.23742	−	0.128619i
$342$	7.84665	+	0.270998i	0.424298	+	0.0146539i
$343$	−16.1831	+	7.11609i	−0.873803	+	0.384233i
$344$	3.44591	−	2.65203i	0.185791	−	0.142988i
$345$	2.41148	+	0.250651i	0.129830	+	0.0134946i
$346$	0.663494	−	12.8011i	0.0356697	−	0.688194i
$347$	1.85802	+	0.0641700i	0.0997439	+	0.00344483i	0.0843451	−	0.996437i	$-0.473120\pi$
$347$	1.85802	+	0.0641700i	0.0997439	+	0.00344483i	0.0153988	+	0.999881i	$0.495098\pi$
$348$	−37.2964	+	9.19274i	−1.99930	+	0.492783i
$349$	1.16791	+	1.27333i	0.0625170	+	0.0681597i	0.767423	−	0.641141i	$-0.221538\pi$
$349$	1.16791	+	1.27333i	0.0625170	+	0.0681597i	−0.704906	+	0.709300i	$0.749011\pi$
$350$	−19.9346	−	28.8802i	−1.06555	−	1.54371i
$351$	2.25940	−	9.89908i	0.120598	−	0.528374i
$352$	14.3814	−	16.8091i	0.766531	−	0.895925i
$353$	−3.52364	+	29.0198i	−0.187545	+	1.54457i	0.529964	+	0.848020i	$0.322205\pi$
$353$	−3.52364	+	29.0198i	−0.187545	+	1.54457i	−0.717509	+	0.696549i	$0.754718\pi$
$354$	39.4571	+	32.5959i	2.09712	+	1.73245i
$355$	−3.09481	−	10.2420i	−0.164255	−	0.543588i
$356$	−12.0041	−	7.98350i	−0.636218	−	0.423125i
$357$	55.5799	+	31.6641i	2.94160	+	1.67584i
$358$	16.1851	+	15.3679i	0.855408	+	0.812219i
$359$	−13.5300	−	26.8976i	−0.714087	−	1.41960i	−0.899491	−	0.436939i	$-0.856063\pi$
$359$	−13.5300	−	26.8976i	−0.714087	−	1.41960i	0.185404	−	0.982662i	$-0.440641\pi$
$360$	−3.62491	+	1.74567i	−0.191050	+	0.0920047i
$361$	−8.15848	+	16.2190i	−0.429393	+	0.853632i
$362$	−6.05556	+	31.5079i	−0.318273	+	1.65602i
$363$	0.557179	−	2.10361i	0.0292443	−	0.110411i
$364$	−11.6043	+	3.72622i	−0.608230	+	0.195307i
$365$	−1.53239	+	6.71384i	−0.0802090	+	0.351418i
$366$	7.89405	+	6.99352i	0.412629	+	0.365557i
$367$	1.39344	−	16.1049i	0.0727369	−	0.840671i	−0.866897	−	0.498488i	$-0.833889\pi$
$367$	1.39344	−	16.1049i	0.0727369	−	0.840671i	0.939633	−	0.342183i	$-0.111166\pi$
$368$	5.95356	−	1.68740i	0.310351	−	0.0879619i
$369$	22.8269	−	10.9929i	1.18832	−	0.572266i
$370$	0.338295	−	0.121662i	0.0175871	−	0.00632490i
$371$	−14.6209	−	42.9702i	−0.759078	−	2.23090i
$372$	24.4268	−	1.68926i	1.26647	−	0.0875840i
$373$	9.28880	−	30.7404i	0.480956	−	1.59168i	−0.291473	−	0.956579i	$-0.594146\pi$
$373$	9.28880	−	30.7404i	0.480956	−	1.59168i	0.772430	−	0.635100i	$-0.219041\pi$
$374$	−28.2004	−	18.7550i	−1.45821	−	0.969800i
$375$	−2.20231	−	18.1377i	−0.113727	−	0.936625i
$376$	5.91093	−	9.22939i	0.304833	−	0.475970i
$377$	21.1413	+	8.43805i	1.08883	+	0.434582i
$378$	−8.08857	+	35.4383i	−0.416031	+	1.82275i
$379$	−11.1853	−	26.6775i	−0.574551	−	1.37033i	−0.904556	−	0.426354i	$-0.859798\pi$
$379$	−11.1853	−	26.6775i	−0.574551	−	1.37033i	0.330005	−	0.943979i	$-0.392950\pi$
$380$	−0.0144858	−	0.839112i	−0.000743104	−	0.0430455i
$381$	−0.573879	−	11.0722i	−0.0294007	−	0.567244i
$382$	1.03754	−	20.0177i	0.0530849	−	1.02420i
$383$	0.263798	−	0.482210i	0.0134794	−	0.0246398i	−0.870476	−	0.492210i	$-0.836189\pi$
$383$	0.263798	−	0.482210i	0.0134794	−	0.0246398i	0.883956	+	0.467570i	$0.154871\pi$
$384$	−17.5150	+	19.0959i	−0.893808	+	0.974482i
$385$	10.0250	+	1.39324i	0.510921	+	0.0710060i
$386$	−3.27895	+	20.9363i	−0.166894	+	1.06563i
$387$	7.89217	−	14.4265i	0.401182	−	0.733341i
$388$	9.07602	−	3.99095i	0.460765	−	0.202610i
$389$	−10.5934	−	4.65817i	−0.537105	−	0.236178i	0.116263	−	0.993218i	$-0.462908\pi$
$389$	−10.5934	−	4.65817i	−0.537105	−	0.236178i	−0.653368	+	0.757040i	$0.726645\pi$
$390$	−7.46789	−	1.30203i	−0.378151	−	0.0659307i
$391$	−2.64526	−	6.30907i	−0.133776	−	0.319063i
$392$	−13.1622	+	4.22647i	−0.664790	+	0.213469i
$393$	−0.713702	−	1.54990i	−0.0360015	−	0.0781820i
$394$	−11.7237	+	25.4597i	−0.590634	+	1.28264i
$395$	1.32390	−	0.880473i	0.0666124	−	0.0443014i
$396$	6.14342	−	20.3311i	0.308718	−	1.02167i
$397$	2.38624	−	1.97130i	0.119762	−	0.0989365i	−0.575087	−	0.818092i	$-0.695032\pi$
$397$	2.38624	−	1.97130i	0.119762	−	0.0989365i	0.694849	+	0.719156i	$0.255471\pi$
$398$	24.0591	+	24.4781i	1.20598	+	1.22697i
$399$	8.60382	+	6.62162i	0.430730	+	0.331496i
$400$	−10.6276	−	19.4268i	−0.531382	−	0.971342i
$401$	36.9989	−	13.3060i	1.84764	−	0.664470i	0.859452	−	0.511217i	$-0.170805\pi$
$401$	36.9989	−	13.3060i	1.84764	−	0.664470i	0.988187	−	0.153254i	$-0.0489752\pi$
$402$	−33.4449	+	17.5532i	−1.66808	+	0.875476i
$403$	−12.3519	−	7.61332i	−0.615292	−	0.379246i
$404$	−3.38410	−	7.34902i	−0.168365	−	0.365628i
$405$	0.486362	−	0.568462i	0.0241675	−	0.0282471i
$406$	−75.6851	−	30.2079i	−3.75619	−	1.49919i
$407$	0.378466	−	0.902661i	0.0187599	−	0.0447433i
$408$	15.1362	+	10.8382i	0.749352	+	0.536570i
$409$	−3.38558	−	6.73052i	−0.167406	−	0.332803i	0.794008	−	0.607907i	$-0.207991\pi$
$409$	−3.38558	−	6.73052i	−0.167406	−	0.332803i	−0.961414	+	0.275105i	$0.911288\pi$
$410$	−3.26987	−	5.97717i	−0.161487	−	0.295191i
$411$	45.3359	−	40.1641i	2.23625	−	1.98115i
$412$	1.25406	+	1.68900i	0.0617832	+	0.0832112i
$413$	11.0502	+	41.7197i	0.543746	+	2.05289i
$414$	8.32099	−	6.87405i	0.408954	−	0.337841i
$415$	5.78290	+	3.29454i	0.283872	+	0.161723i
$416$	−13.6730	+	2.87341i	−0.670373	+	0.140880i
$417$	8.39833	−	20.0304i	0.411268	−	0.980894i
$418$	−4.30262	−	3.81179i	−0.210448	−	0.186441i
$419$	−3.14807	−	4.56077i	−0.153793	−	0.222808i	0.738512	−	0.674240i	$-0.235529\pi$
$419$	−3.14807	−	4.56077i	−0.153793	−	0.222808i	−0.892305	+	0.451432i	$0.850913\pi$
$420$	10.6270	+	1.85281i	0.518543	+	0.0904080i
$421$	−17.9628	−	8.65045i	−0.875455	−	0.421597i	−0.0584927	−	0.998288i	$-0.518629\pi$
$421$	−17.9628	−	8.65045i	−0.875455	−	0.421597i	−0.816962	+	0.576691i	$0.804344\pi$
$422$	−18.2902	−	1.90110i	−0.890352	−	0.0925439i
$423$	6.41321	−	40.9488i	0.311821	−	1.99100i
$424$	−2.93946	−	12.8786i	−0.142753	−	0.625440i
$425$	−19.9044	+	14.2525i	−0.965505	+	0.691345i
$426$	−69.1589	−	36.2974i	−3.35076	−	1.75861i
$427$	1.97897	+	8.67045i	0.0957693	+	0.419593i
$428$	0.744308	−	0.811488i	0.0359775	−	0.0392247i
$429$	−16.3557	+	12.5876i	−0.789662	+	0.607736i
$430$	−3.98410	−	1.91864i	−0.192130	−	0.0925251i
$431$	0.526649	+	30.5070i	0.0253678	+	1.46947i	0.690818	+	0.723029i	$0.257251\pi$
$431$	0.526649	+	30.5070i	0.0253678	+	1.46947i	−0.665450	+	0.746442i	$0.731760\pi$
$432$	−7.38860	+	21.7148i	−0.355484	+	1.04475i
$433$	3.76959	−	14.2320i	0.181155	−	0.683945i	−0.813579	−	0.581455i	$-0.802484\pi$
$433$	3.76959	−	14.2320i	0.181155	−	0.683945i	0.994734	−	0.102490i	$-0.0326810\pi$
$434$	44.2193	+	27.2554i	2.12260	+	1.30830i
$435$	−13.0977	−	15.3087i	−0.627989	−	0.733997i
$436$	16.0524	−	1.11012i	0.768773	−	0.0531652i
$437$	−0.297295	−	1.12243i	−0.0142215	−	0.0536929i
$438$	27.1125	+	42.3337i	1.29548	+	2.02278i
$439$	12.3421	−	2.15185i	0.589057	−	0.102702i	0.130625	−	0.991432i	$-0.458302\pi$
$439$	12.3421	−	2.15185i	0.589057	−	0.102702i	0.458431	+	0.888730i	$0.348411\pi$
$440$	2.86004	+	0.704937i	0.136347	+	0.0336066i
$441$	−39.1317	+	34.6677i	−1.86341	+	1.65084i
$442$	6.89021	+	20.2500i	0.327734	+	0.963197i
$443$	−16.4212	−	19.1932i	−0.780195	−	0.911896i	0.217748	−	0.976005i	$-0.430129\pi$
$443$	−16.4212	−	19.1932i	−0.780195	−	0.911896i	−0.997943	+	0.0641088i	$0.979580\pi$
$444$	0.436334	−	0.947556i	0.0207075	−	0.0449690i
$445$	0.911421	−	7.50623i	0.0432055	−	0.355829i
$446$	8.99693	−	12.1173i	0.426017	−	0.573770i
$447$	−7.97116	+	12.4463i	−0.377023	+	0.588688i
$448$	8.10815	−	1.70395i	0.383074	−	0.0805039i
$449$	−22.6459	−	21.5025i	−1.06873	−	1.01477i	−0.999853	−	0.0171426i	$-0.994543\pi$
$449$	−22.6459	−	21.5025i	−1.06873	−	1.01477i	−0.0688734	−	0.997625i	$-0.521940\pi$
$450$	−30.6077	−	23.5562i	−1.44286	−	1.11045i
$451$	−18.0104	−	4.43916i	−0.848075	−	0.209032i
$452$	21.3482	−	12.1622i	1.00414	−	0.572060i
$453$	−31.1989	−	2.15759i	−1.46585	−	0.101372i
$454$	−9.77896	−	15.2690i	−0.458949	−	0.716609i
$455$	−4.48097	−	4.55899i	−0.210071	−	0.213729i
$456$	2.29134	+	2.17565i	0.107302	+	0.101884i
$457$	−2.74328	−	1.96432i	−0.128325	−	0.0918868i	0.516207	−	0.856464i	$-0.327344\pi$
$457$	−2.74328	−	1.96432i	−0.128325	−	0.0918868i	−0.644532	+	0.764577i	$0.722948\pi$
$458$	−1.07034	+	12.3707i	−0.0500138	+	0.578045i
$459$	24.8162	+	5.21518i	1.15832	+	0.243424i
$460$	−0.779828	−	0.850214i	−0.0363597	−	0.0396414i
$461$	25.0395	+	11.0105i	1.16621	+	0.512809i	0.893401	−	0.449260i	$-0.148312\pi$
$461$	25.0395	+	11.0105i	1.16621	+	0.512809i	0.272805	+	0.962069i	$0.412049\pi$
$462$	58.5529	−	45.0632i	2.72413	−	2.09653i
$463$	20.3303	+	2.82543i	0.944829	+	0.131309i	0.593402	−	0.804906i	$-0.297784\pi$
$463$	20.3303	+	2.82543i	0.944829	+	0.131309i	0.351427	+	0.936215i	$0.385697\pi$
$464$	−45.5322	−	23.8972i	−2.11378	−	1.10940i
$465$	6.54871	+	11.0471i	0.303689	+	0.512298i
$466$	−23.7265	+	29.7521i	−1.09911	+	1.37824i
$467$	−16.2740	−	27.4530i	−0.753073	−	1.27037i	−0.956629	−	0.291309i	$-0.905909\pi$
$467$	−16.2740	−	27.4530i	−0.753073	−	1.27037i	0.203556	−	0.979063i	$-0.434750\pi$
$468$	−10.9065	+	7.80952i	−0.504151	+	0.360995i
$469$	−31.5483	−	4.38448i	−1.45677	−	0.202456i
$470$	−11.0861	−	1.15230i	−0.511363	−	0.0531515i
$471$	2.90909	+	56.1267i	0.134044	+	2.58618i
$472$	1.94347	+	12.4092i	0.0894556	+	0.571180i
$473$	−11.1816	+	4.46288i	−0.514132	+	0.205204i
$474$	2.19061	−	11.3980i	0.100618	−	0.523530i
$475$	−3.67913	+	1.93096i	−0.168810	+	0.0885984i
$476$	−9.80492	−	28.8163i	−0.449408	−	1.32079i
$477$	−29.7806	−	40.1092i	−1.36356	−	1.83648i
$478$	10.6970	+	0.739759i	0.489268	+	0.0338358i
$479$	−7.46973	−	38.8660i	−0.341301	−	1.77583i	−0.590151	−	0.807293i	$-0.700932\pi$
$479$	−7.46973	−	38.8660i	−0.341301	−	1.77583i	0.248851	−	0.968542i	$-0.419947\pi$
$480$	11.8974	+	3.37206i	0.543041	+	0.153913i
$481$	−0.537136	+	0.306008i	−0.0244913	+	0.0139528i
$482$	10.0618	+	13.5515i	0.458304	+	0.617256i
$483$	14.8892	−	1.02968i	0.677483	−	0.0468520i
$484$	−0.862245	+	0.573446i	−0.0391929	+	0.0260657i
$485$	4.00911	+	3.31197i	0.182045	+	0.150389i
$486$	−2.67724	−	30.9427i	−0.121442	−	1.40359i
$487$	−5.77223	−	1.85351i	−0.261565	−	0.0839904i	0.172051	−	0.985088i	$-0.444960\pi$
$487$	−5.77223	−	1.85351i	−0.261565	−	0.0839904i	−0.433616	+	0.901098i	$0.642763\pi$
$488$	0.311982	+	2.56940i	0.0141228	+	0.116311i
$489$	36.0207	+	20.5211i	1.62891	+	0.927997i
$490$	9.85470	+	10.0263i	0.445190	+	0.452942i
$491$	4.54078	−	0.791685i	0.204922	−	0.0357282i	−0.0683664	−	0.997660i	$-0.521779\pi$
$491$	4.54078	−	0.791685i	0.204922	−	0.0357282i	0.273289	+	0.961932i	$0.411889\pi$
$492$	−19.0206	−	5.39096i	−0.857516	−	0.243043i
$493$	−20.1592	+	53.1553i	−0.907923	+	2.39400i
$494$	0.685209	+	3.56523i	0.0308290	+	0.160408i
$495$	10.9741	−	1.91334i	0.493251	−	0.0859984i
$496$	25.9757	+	19.9913i	1.16634	+	0.897636i
$497$	−29.5974	−	58.8394i	−1.32762	−	2.63931i
$498$	46.7442	−	13.2486i	2.09466	−	0.593683i
$499$	−7.91321	+	8.05100i	−0.354244	+	0.360412i	−0.867163	−	0.498025i	$-0.834059\pi$
$499$	−7.91321	+	8.05100i	−0.354244	+	0.360412i	0.512919	+	0.858437i	$0.328564\pi$
$500$	−4.93888	+	7.15521i	−0.220874	+	0.319991i
$501$	32.2544	−	7.95000i	1.44102	−	0.355180i
$502$	−10.5044	+	4.61904i	−0.468835	+	0.206158i
$503$	−20.6532	+	22.5173i	−0.920880	+	1.00400i	0.0790946	+	0.996867i	$0.474797\pi$
$503$	−20.6532	+	22.5173i	−0.920880	+	1.00400i	−0.999975	+	0.00713012i	$0.997730\pi$
$504$	−20.1372	+	14.4192i	−0.896983	+	0.642281i
$505$	2.64581	−	3.31774i	0.117737	−	0.147637i
$506$	−7.90203			−0.351288
$507$	−23.0124			−1.02202
$508$	−3.28939	+	4.12477i	−0.145943	+	0.183007i
$509$	33.9709	+	17.8293i	1.50573	+	0.790270i	0.997481	−	0.0709378i	$-0.0225992\pi$
$509$	33.9709	+	17.8293i	1.50573	+	0.790270i	0.508253	+	0.861208i	$0.330291\pi$
$510$	2.92935	−	18.7041i	0.129714	−	0.828230i
$511$	−2.19430	+	42.3357i	−0.0970700	+	1.87282i
$512$	19.3128	−	2.00739i	0.853512	−	0.0887148i
$513$	4.05003	+	1.45652i	0.178813	+	0.0643070i
$514$	−0.765976	+	44.3704i	−0.0337858	+	1.95710i
$515$	−0.495816	+	0.985679i	−0.0218483	+	0.0434342i
$516$	−12.0744	+	4.34235i	−0.531546	+	0.191161i
$517$	−22.7140	+	20.1228i	−0.998958	+	0.885000i
$518$	1.92293	−	1.09550i	0.0844885	−	0.0481334i
$519$	6.91787	−	18.2409i	0.303661	−	0.800688i
$520$	−1.15995	−	1.45453i	−0.0508671	−	0.0637853i
$521$	−9.75071	+	25.7105i	−0.427186	+	1.12640i	0.532773	+	0.846258i	$0.321150\pi$
$521$	−9.75071	+	25.7105i	−0.427186	+	1.12640i	−0.959959	+	0.280140i	$0.909619\pi$
$522$	−89.4763	−	6.18781i	−3.91627	−	0.270833i
$523$	7.62064	+	28.7714i	0.333227	+	1.25809i	0.900608	+	0.434632i	$0.143122\pi$
$523$	7.62064	+	28.7714i	0.333227	+	1.25809i	−0.567381	+	0.823455i	$0.692043\pi$
$524$	−0.234861	+	0.777249i	−0.0102599	+	0.0339543i
$525$	−15.4484	−	51.1249i	−0.674221	−	2.23127i
$526$	7.16728	+	18.8986i	0.312508	+	0.824017i
$527$	18.4786	−	31.1719i	0.804942	−	1.35787i
$528$	39.6899	−	24.4636i	1.72728	−	1.06464i
$529$	17.8222	+	11.8529i	0.774880	+	0.515343i
$530$	−10.3568	+	8.55588i	−0.449872	+	0.371644i
$531$	25.6181	+	40.0004i	1.11173	+	1.73587i
$532$	−0.975067	−	5.07341i	−0.0422745	−	0.219960i
$533$	7.30446	+	9.15951i	0.316391	+	0.396742i
$534$	−34.4154	−	43.1556i	−1.48930	−	1.86752i
$535$	0.555652	+	0.157487i	0.0240230	+	0.00680876i
$536$	−9.00046	−	2.21841i	−0.388761	−	0.0958209i
$537$	16.3024	+	29.8001i	0.703502	+	1.28597i
$538$	−3.75500	+	1.80831i	−0.161890	+	0.0779619i
$539$	38.2528	−	1.32113i	1.64767	−	0.0569050i
$540$	4.23568	−	0.588660i	0.182275	−	0.0253319i
$541$	24.2946	−	23.0680i	1.04451	−	0.991773i	0.0445346	−	0.999008i	$-0.485819\pi$
$541$	24.2946	−	23.0680i	1.04451	−	0.991773i	0.999974	+	0.00723507i	$0.00230302\pi$
$542$	−10.6148	−	0.366601i	−0.455946	−	0.0157469i
$543$	−23.4357	+	42.8393i	−1.00572	+	1.83841i
$544$	−7.76455	−	34.0187i	−0.332902	−	1.45854i
$545$	4.30358	+	7.25978i	0.184345	+	0.310975i
$546$	−46.6650			−1.99708
$547$	−22.1298	−	7.56784i	−0.946202	−	0.323578i
$547$	−22.1298	−	7.56784i	−0.946202	−	0.323578i
$548$	−28.8214			−1.23119
$549$	4.99134	+	8.41998i	0.213025	+	0.359356i
$550$	6.29226	+	27.5682i	0.268303	+	1.17551i
$551$	−4.63087	+	8.46501i	−0.197282	+	0.360622i
$552$	4.34101	+	0.149924i	0.184766	+	0.00638120i
$553$	7.09770	−	6.73935i	0.301825	−	0.286586i
$554$	11.9077	−	1.65489i	0.505909	−	0.0703095i
$555$	0.546821	−	0.0188854i	0.0232113	−	0.000801640i
$556$	−9.31188	+	4.48436i	−0.394912	+	0.190179i
$557$	5.20032	+	9.50593i	0.220345	+	0.402779i	0.964047	−	0.265731i	$-0.0856134\pi$
$557$	5.20032	+	9.50593i	0.220345	+	0.402779i	−0.743703	+	0.668511i	$0.766932\pi$
$558$	55.5093	+	13.6818i	2.34990	+	0.579198i
$559$	7.31568	+	2.07346i	0.309420	+	0.0876982i
$560$	9.00366	+	11.2902i	0.380474	+	0.477099i
$561$	−32.1374	−	40.2990i	−1.35684	−	1.70143i
$562$	0.399237	+	2.07728i	0.0168408	+	0.0876249i
$563$	11.2472	+	17.5615i	0.474013	+	0.740129i	0.993436	−	0.114388i	$-0.0364907\pi$
$563$	11.2472	+	17.5615i	0.474013	+	0.740129i	−0.519424	+	0.854517i	$0.673853\pi$
$564$	−24.9343	+	20.5984i	−1.04992	+	0.867350i
$565$	10.7302	+	7.13626i	0.451424	+	0.300225i
$566$	19.8823	−	12.2548i	0.835715	−	0.515108i
$567$	2.34845	−	3.96164i	0.0986255	−	0.166373i
$568$	−6.79727	−	17.9229i	−0.285207	−	0.752029i
$569$	−2.58256	−	8.54674i	−0.108266	−	0.358298i	0.886207	−	0.463290i	$-0.153331\pi$
$569$	−2.58256	−	8.54674i	−0.108266	−	0.358298i	−0.994473	+	0.104993i	$0.966518\pi$
$570$	0.929447	−	3.07592i	0.0389303	−	0.128836i
$571$	2.35473	+	8.89020i	0.0985424	+	0.372043i	0.997870	−	0.0652319i	$-0.0207787\pi$
$571$	2.35473	+	8.89020i	0.0985424	+	0.372043i	−0.899328	+	0.437275i	$0.855944\pi$
$572$	9.79758	+	0.677561i	0.409657	+	0.0283302i
$573$	10.8178	−	28.5242i	0.451920	−	1.19161i
$574$	−26.1497	−	32.7907i	−1.09147	−	1.36866i
$575$	−2.02547	+	5.34074i	−0.0844681	+	0.222724i
$576$	7.92329	−	4.51393i	0.330137	−	0.188080i
$577$	4.42034	−	3.91608i	0.184021	−	0.163029i	−0.566083	−	0.824348i	$-0.691542\pi$
$577$	4.42034	−	3.91608i	0.184021	−	0.163029i	0.750104	+	0.661320i	$0.230003\pi$
$578$	−21.1235	+	7.59668i	−0.878621	+	0.315980i
$579$	−14.4932	+	28.8123i	−0.602316	+	1.19740i
$580$	−0.165479	+	9.58563i	−0.00687113	+	0.398021i
$581$	38.5533	+	13.8650i	1.59946	+	0.575218i
$582$	37.7582	−	3.92462i	1.56513	−	0.162681i
$583$	−1.89316	+	36.5258i	−0.0784067	+	1.51274i
$584$	−1.90899	+	12.1890i	−0.0789946	+	0.504386i
$585$	−6.22974	−	3.26962i	−0.257568	−	0.135182i
$586$	−25.5577	+	32.0483i	−1.05578	+	1.32390i
$587$	−2.68068			−0.110644			−0.0553218	−	0.998469i	$-0.517618\pi$
$587$	−2.68068			−0.110644			−0.0553218	+	0.998469i	$0.517618\pi$
$588$	40.7940			1.68232
$589$	3.83474	−	4.80862i	0.158008	−	0.198136i
$590$	10.3855	−	7.43652i	0.427566	−	0.306157i
$591$	−28.8349	+	31.4375i	−1.18611	+	1.29317i
$592$	1.27837	−	0.562131i	0.0525407	−	0.0231034i
$593$	−4.00090	+	0.986134i	−0.164297	+	0.0404957i	−0.320606	−	0.947213i	$-0.603887\pi$
$593$	−4.00090	+	0.986134i	−0.164297	+	0.0404957i	0.156309	+	0.987708i	$0.450040\pi$
$594$	16.6389	−	24.1056i	0.682704	−	0.989067i
$595$	11.1910	−	11.3859i	0.458787	−	0.466776i
$596$	6.76656	−	1.91783i	0.277169	−	0.0785573i
$597$	23.4735	+	46.6651i	0.960705	+	1.90987i
$598$	3.95507	+	3.04388i	0.161735	+	0.124474i
$599$	−21.6148	+	3.76854i	−0.883156	+	0.153978i	−0.595116	−	0.803640i	$-0.702894\pi$
$599$	−21.6148	+	3.76854i	−0.883156	+	0.153978i	−0.288040	+	0.957618i	$0.593004\pi$
$600$	−2.93363	−	15.2641i	−0.119765	−	0.623153i
$601$	5.85806	−	15.4464i	0.238955	−	0.630074i	−0.760867	−	0.648908i	$-0.775226\pi$
$601$	5.85806	−	15.4464i	0.238955	−	0.630074i	0.999823	+	0.0188340i	$0.00599542\pi$
$602$	−26.1899	−	7.42292i	−1.06742	−	0.302536i
$603$	−34.5353	+	6.02123i	−1.40639	+	0.245203i
$604$	10.4316	+	10.6132i	0.424455	+	0.431846i
$605$	−0.471914	−	0.268851i	−0.0191860	−	0.0109304i
$606$	−3.73398	−	30.7521i	−0.151683	−	1.24922i
$607$	−5.49711	−	1.76516i	−0.223121	−	0.0716457i	0.192065	−	0.981382i	$-0.438481\pi$
$607$	−5.49711	−	1.76516i	−0.223121	−	0.0716457i	−0.415186	+	0.909736i	$0.636284\pi$
$608$	−0.510511	−	5.90033i	−0.0207039	−	0.239290i
$609$	−95.6166	−	78.9898i	−3.87458	−	3.20083i
$610$	2.19171	−	1.45763i	0.0887399	−	0.0590176i
$611$	19.1200	−	1.32226i	0.773513	−	0.0534930i
$612$	−19.9712	−	26.8977i	−0.807287	−	1.08727i
$613$	−24.3077	+	13.8482i	−0.981778	+	0.559323i	−0.899329	−	0.437273i	$-0.855944\pi$
$613$	−24.3077	+	13.8482i	−0.981778	+	0.559323i	−0.0824489	+	0.996595i	$0.526274\pi$
$614$	−55.2760	−	15.6667i	−2.23076	−	0.632257i
$615$	−1.95705	−	10.1828i	−0.0789157	−	0.410609i
$616$	18.0898	+	1.25102i	0.728860	+	0.0504050i
$617$	−3.00039	−	4.04100i	−0.120791	−	0.162685i	0.738359	−	0.674408i	$-0.235601\pi$
$617$	−3.00039	−	4.04100i	−0.120791	−	0.162685i	−0.859151	+	0.511723i	$0.829007\pi$
$618$	2.59453	+	7.62521i	0.104367	+	0.306731i
$619$	27.4911	−	14.4285i	1.10496	−	0.579928i	0.189316	−	0.981916i	$-0.439373\pi$
$619$	27.4911	−	14.4285i	1.10496	−	0.579928i	0.915645	+	0.401988i	$0.131681\pi$
$620$	1.15338	−	6.00120i	0.0463209	−	0.241014i
$621$	5.49510	−	2.19324i	0.220511	−	0.0880116i
$622$	−2.07919	−	13.2758i	−0.0833679	−	0.532310i
$623$	−2.40933	−	46.4845i	−0.0965279	−	1.86236i
$624$	−29.2888	−	3.04430i	−1.17249	−	0.121870i
$625$	17.8734	+	2.48399i	0.714937	+	0.0993595i
$626$	42.7784	−	30.6313i	1.70977	−	1.22427i
$627$	−4.46112	−	7.52555i	−0.178160	−	0.300541i
$628$	16.6745	−	20.9092i	0.665385	−	0.834367i
$629$	−0.787283	−	1.32808i	−0.0313910	−	0.0529541i
$630$	22.3022	+	11.7051i	0.888543	+	0.466343i
$631$	−26.0539	−	3.62088i	−1.03719	−	0.144145i	−0.401318	−	0.915939i	$-0.631448\pi$
$631$	−26.0539	−	3.62088i	−1.03719	−	0.144145i	−0.635873	+	0.771794i	$0.719360\pi$
$632$	2.25737	−	1.73730i	0.0897932	−	0.0691062i
$633$	−25.6190	−	11.2653i	−1.01826	−	0.447756i
$634$	−19.0381	−	20.7565i	−0.756101	−	0.824346i
$635$	−2.70796	−	0.569083i	−0.107462	−	0.0225834i
$636$	−3.36020	+	38.8362i	−0.133241	+	1.53995i
$637$	−19.6550	−	14.0739i	−0.778759	−	0.557627i
$638$	47.6189	+	45.2147i	1.88525	+	1.79007i
$639$	−50.8145	−	51.6993i	−2.01019	−	2.04519i
$640$	3.48784	+	5.44596i	0.137869	+	0.215271i
$641$	27.9409	+	1.93228i	1.10360	+	0.0763204i	0.609276	−	0.792958i	$-0.291460\pi$
$641$	27.9409	+	1.93228i	1.10360	+	0.0763204i	0.494323	+	0.869278i	$0.335416\pi$
$642$	3.66327	−	2.08698i	0.144578	−	0.0823666i
$643$	14.3024	+	3.52523i	0.564032	+	0.139021i	0.511014	−	0.859572i	$-0.329270\pi$
$643$	14.3024	+	3.52523i	0.564032	+	0.139021i	0.0530175	+	0.998594i	$0.483116\pi$
$644$	−5.62816	−	4.33151i	−0.221780	−	0.170686i
$645$	−4.88046	−	4.63405i	−0.192168	−	0.182466i
$646$	−8.87315	+	1.86471i	−0.349110	+	0.0733661i
$647$	17.9482	−	28.0246i	0.705618	−	1.10176i	−0.284109	−	0.958792i	$-0.591698\pi$
$647$	17.9482	−	28.0246i	0.705618	−	1.10176i	0.989727	−	0.142969i	$-0.0456650\pi$
$648$	0.799010	−	1.07613i	0.0313881	−	0.0422742i
$649$	4.19190	−	34.5234i	0.164546	−	1.35516i
$650$	7.46999	−	16.2221i	0.292997	−	0.636282i
$651$	51.3946	+	60.0702i	2.01431	+	2.35434i
$652$	−6.35445	−	18.6755i	−0.248859	−	0.731388i
$653$	−17.0323	+	15.0893i	−0.666525	+	0.590490i	−0.927032	−	0.374982i	$-0.877649\pi$
$653$	−17.0323	+	15.0893i	−0.666525	+	0.590490i	0.260507	+	0.965472i	$0.416110\pi$
$654$	59.8183	+	14.7439i	2.33908	+	0.576532i
$655$	−0.419538	+	0.0731464i	−0.0163927	+	0.00285807i
$656$	−14.2734	−	22.2867i	−0.557283	−	0.870148i
$657$	11.9462	+	45.1026i	0.466067	+	1.75962i
$658$	−68.4490	+	4.73365i	−2.66842	+	0.184537i
$659$	26.6917	+	31.1974i	1.03976	+	1.21528i	0.976103	+	0.217308i	$0.0697277\pi$
$659$	26.6917	+	31.1974i	1.03976	+	1.21528i	0.0636596	+	0.997972i	$0.479723\pi$
$660$	−7.39969	−	4.56093i	−0.288032	−	0.177534i
$661$	5.04950	−	19.0642i	0.196403	−	0.741512i	−0.794538	−	0.607214i	$-0.792287\pi$
$661$	5.04950	−	19.0642i	0.196403	−	0.741512i	0.990941	−	0.134298i	$-0.0428778\pi$
$662$	−0.903456	+	2.65522i	−0.0351138	+	0.103198i
$663$	0.561911	+	32.5496i	0.0218228	+	1.26412i
$664$	10.7430	+	5.17354i	0.416908	+	0.200772i
$665$	2.14735	−	1.65263i	0.0832705	−	0.0640863i
$666$	1.64643	−	1.79504i	0.0637980	−	0.0695564i
$667$	2.95157	+	12.9317i	0.114285	+	0.500716i
$668$	−13.9970	−	7.34619i	−0.541560	−	0.284232i
$669$	18.6753	−	13.3724i	0.722030	−	0.517007i
$670$	2.09771	+	9.19066i	0.0810415	+	0.355066i
$671$	1.10884	−	7.08001i	0.0428063	−	0.273321i
$672$	75.7163	+	7.87002i	2.92082	+	0.303593i
$673$	22.7031	+	10.9332i	0.875140	+	0.421445i	0.816847	−	0.576854i	$-0.195720\pi$
$673$	22.7031	+	10.9332i	0.875140	+	0.421445i	0.0582931	+	0.998300i	$0.481434\pi$
$674$	37.1398	+	6.47533i	1.43057	+	0.249420i
$675$	−12.0273	−	17.4246i	−0.462932	−	0.670673i
$676$	8.19657	+	7.26152i	0.315253	+	0.279289i
$677$	−9.32288	+	22.2355i	−0.358308	+	0.854581i	0.638105	+	0.769950i	$0.279719\pi$
$677$	−9.32288	+	22.2355i	−0.358308	+	0.854581i	−0.996412	+	0.0846318i	$0.973029\pi$
$678$	92.0613	−	19.3469i	3.53559	−	0.743013i
$679$	27.8148	+	15.8462i	1.06743	+	0.608121i
$680$	3.58208	−	2.95919i	0.137366	−	0.113480i
$681$	−7.06560	−	26.6759i	−0.270754	−	1.02222i
$682$	−24.9521	−	33.6061i	−0.955466	−	1.28684i
$683$	14.7741	−	13.0887i	0.565316	−	0.500826i	−0.331366	−	0.943502i	$-0.607509\pi$
$683$	14.7741	−	13.0887i	0.565316	−	0.500826i	0.896682	+	0.442676i	$0.145971\pi$
$684$	−2.72895	−	4.98839i	−0.104344	−	0.190736i
$685$	−6.79297	−	13.5044i	−0.259546	−	0.515976i
$686$	26.1880	+	18.7518i	0.999861	+	0.715946i
$687$	−7.30713	+	17.4279i	−0.278785	+	0.664915i
$688$	−15.9535	−	6.36748i	−0.608223	−	0.242758i
$689$	15.0174	−	17.5524i	0.572117	−	0.668694i
$690$	−1.84759	−	4.01229i	−0.0703367	−	0.152745i
$691$	−7.12888	−	4.39401i	−0.271195	−	0.167156i	0.382408	−	0.923994i	$-0.375095\pi$
$691$	−7.12888	−	4.39401i	−0.271195	−	0.167156i	−0.653603	+	0.756838i	$0.726743\pi$
$692$	−8.21990	+	4.31413i	−0.312474	+	0.163999i
$693$	64.5287	−	23.2066i	2.45124	−	0.881546i
$694$	−1.62566	−	2.97163i	−0.0617092	−	0.112801i
$695$	−4.29590	−	3.30619i	−0.162953	−	0.125411i
$696$	−25.3017	−	25.7423i	−0.959060	−	0.975760i
$697$	−22.5572	+	18.6347i	−0.854414	+	0.705840i
$698$	0.910567	−	3.01344i	0.0344655	−	0.114060i
$699$	−48.2249	+	32.0726i	−1.82403	+	1.21310i
$700$	−10.6300	+	23.0844i	−0.401775	+	0.872507i
$701$	12.0880	+	26.2506i	0.456556	+	0.991472i	0.989394	+	0.145254i	$0.0464001\pi$
$701$	12.0880	+	26.2506i	0.456556	+	0.991472i	−0.532838	+	0.846217i	$0.678875\pi$
$702$	−17.6136	+	5.65585i	−0.664782	+	0.213466i
$703$	−0.101322	−	0.241659i	−0.00382144	−	0.00911433i
$704$	−6.57704	−	1.14671i	−0.247882	−	0.0432182i
$705$	−15.5283	−	6.82815i	−0.584828	−	0.257163i
$706$	48.7554	−	21.4389i	1.83493	−	0.806865i
$707$	12.5373	−	22.9176i	0.471515	−	0.861906i
$708$	5.73506	−	36.6187i	0.215537	−	1.37622i
$709$	16.4628	+	2.28795i	0.618274	+	0.0859256i	0.439914	−	0.898040i	$-0.355009\pi$
$709$	16.4628	+	2.28795i	0.618274	+	0.0859256i	0.178360	+	0.983965i	$0.442921\pi$
$710$	−13.1766	+	14.3659i	−0.494508	+	0.539142i
$711$	5.17004	−	9.45059i	0.193892	−	0.354425i
$712$	0.701194	−	13.5285i	0.0262783	−	0.507002i
$713$	−0.437639	−	8.44361i	−0.0163897	−	0.316216i
$714$	−2.01162	−	116.527i	−0.0752831	−	4.36089i
$715$	1.99173	+	4.75039i	0.0744866	+	0.177654i
$716$	3.59675	−	15.7584i	0.134417	−	0.588918i
$717$	15.1564	+	6.04931i	0.566025	+	0.225916i
$718$	−29.5853	+	46.1948i	−1.10411	+	1.72398i
$719$	0.879968	+	7.24719i	0.0328173	+	0.270275i	0.999876	+	0.0157227i	$0.00500490\pi$
$719$	0.879968	+	7.24719i	0.0328173	+	0.270275i	−0.967059	+	0.254552i	$0.918072\pi$
$720$	13.2341	+	8.80153i	0.493208	+	0.328014i
$721$	−1.96464	+	6.50181i	−0.0731672	+	0.242140i
$722$	32.9992	−	2.28209i	1.22810	−	0.0849306i
$723$	8.27465	+	24.3188i	0.307737	+	0.904428i
$724$	21.8652	−	7.86342i	0.812612	−	0.292242i
$725$	42.7650	−	20.5946i	1.58825	−	0.764863i
$726$	−3.81456	+	1.08115i	−0.141572	+	0.0401253i
$727$	−2.28982	+	26.4651i	−0.0849249	+	0.981536i	0.824553	+	0.565784i	$0.191426\pi$
$727$	−2.28982	+	26.4651i	−0.0849249	+	0.981536i	−0.909478	+	0.415752i	$0.863519\pi$
$728$	−8.57232	−	7.59441i	−0.317711	−	0.281468i
$729$	9.79663	−	42.9219i	0.362838	−	1.58970i
$730$	11.9460	−	3.83596i	0.442143	−	0.141975i
$731$	−4.86225	+	18.3573i	−0.179837	+	0.678967i
$732$	1.44154	−	7.50056i	0.0532810	−	0.277229i
$733$	6.23887	−	12.4028i	0.230438	−	0.458109i	−0.748262	−	0.663403i	$-0.769112\pi$
$733$	6.23887	−	12.4028i	0.230438	−	0.458109i	0.978700	+	0.205293i	$0.0658149\pi$
$734$	−26.5353	+	12.7787i	−0.979434	+	0.471671i
$735$	9.61480	+	19.1142i	0.354647	+	0.705036i
$736$	−5.90395	−	5.60587i	−0.217623	−	0.206635i
$737$	22.3008	+	12.7049i	0.821462	+	0.467990i
$738$	−38.4365	−	25.5627i	−1.41487	−	0.940974i
$739$	−6.17263	−	20.4277i	−0.227064	−	0.751446i	−0.993967	−	0.109683i	$-0.965016\pi$
$739$	−6.17263	−	20.4277i	−0.227064	−	0.751446i	0.766903	−	0.641763i	$-0.221797\pi$
$740$	−0.200726	−	0.165822i	−0.00737883	−	0.00609572i
$741$	−0.666009	+	5.48508i	−0.0244665	+	0.201499i
$742$	−53.7617	+	62.8370i	−1.97365	+	2.30682i
$743$	7.20390	−	31.5624i	0.264286	−	1.15791i	−0.652265	−	0.757991i	$-0.726181\pi$
$743$	7.20390	−	31.5624i	0.264286	−	1.15791i	0.916550	−	0.399919i	$-0.130962\pi$
$744$	13.0699	+	18.9351i	0.479167	+	0.694193i
$745$	2.49343	+	2.71848i	0.0913520	+	0.0995973i
$746$	−56.8083	+	14.0020i	−2.07990	+	0.512649i
$747$	45.0661	+	1.55643i	1.64888	+	0.0569470i
$748$	−1.26957	+	24.4946i	−0.0464202	+	0.895611i
$749$	3.53622	+	0.367558i	0.129211	+	0.0134303i
$750$	−26.3804	+	20.3027i	−0.963276	+	0.741351i
$751$	29.5610	−	12.9987i	1.07870	−	0.474329i	0.214107	−	0.976810i	$-0.431316\pi$
$751$	29.5610	−	12.9987i	1.07870	−	0.474329i	0.864588	+	0.502481i	$0.167579\pi$
$752$	−43.2701	−	1.49441i	−1.57790	−	0.0544954i
$753$	−17.3708	+	1.80554i	−0.633027	+	0.0657974i
$754$	−6.41708	−	40.9735i	−0.233696	−	1.49217i
$755$	−2.51422	+	7.38920i	−0.0915020	+	0.268921i
$756$	25.0645	−	8.04840i	0.911588	−	0.292717i
$757$	−33.4521	+	39.0989i	−1.21584	+	1.42108i	−0.338658	+	0.940909i	$0.609973\pi$
$757$	−33.4521	+	39.0989i	−1.21584	+	1.42108i	−0.877178	+	0.480166i	$0.840576\pi$
$758$	−31.4188	+	42.3156i	−1.14118	+	1.53697i
$759$	−11.4505	−	3.67685i	−0.415628	−	0.133461i
$760$	0.671323	−	0.413782i	0.0243514	−	0.0150095i
$761$	−4.02601	−	13.3237i	−0.145943	−	0.482984i	0.853320	−	0.521388i	$-0.174586\pi$
$761$	−4.02601	−	13.3237i	−0.145943	−	0.482984i	−0.999262	+	0.0384046i	$0.987772\pi$
$762$	−16.8198	+	11.1862i	−0.609317	+	0.405234i
$763$	33.7747	+	39.4760i	1.22273	+	1.42913i
$764$	−12.8538	+	6.74621i	−0.465035	+	0.244069i
$765$	7.89597	−	15.6971i	0.285479	−	0.567531i
$766$	−1.00084	+	0.0345656i	−0.0361616	+	0.00124890i
$767$	−15.3966	+	15.6647i	−0.555940	+	0.565620i
$768$	56.7557	+	11.9273i	2.04799	+	0.430390i
$769$	0.0232965	+	0.0337508i	0.000840094	+	0.00121709i	0.823404	−	0.567456i	$-0.192072\pi$
$769$	0.0232965	+	0.0337508i	0.000840094	+	0.00121709i	−0.822564	+	0.568673i	$0.807457\pi$
$770$	−7.13033	−	17.0062i	−0.256959	−	0.612861i
$771$	−21.7557	+	63.9391i	−0.783513	+	2.30271i
$772$	14.2539	−	5.68909i	0.513008	−	0.204755i
$773$	−0.369650	+	21.4126i	−0.0132954	+	0.770156i	0.916075	+	0.401007i	$0.131340\pi$
$773$	−0.369650	+	21.4126i	−0.0132954	+	0.770156i	−0.929370	+	0.369149i	$0.879649\pi$
$774$	−29.9425	+	1.03412i	−1.07626	+	0.0371705i
$775$	−29.1092	+	8.25033i	−1.04563	+	0.296361i
$776$	7.57484	+	5.42393i	0.271921	+	0.194708i
$777$	3.29618	−	0.692700i	0.118250	−	0.0248505i
$778$	2.54141	+	20.9304i	0.0911138	+	0.750390i
$779$	−4.22748	+	2.60568i	−0.151465	+	0.0933583i
$780$	1.94676	+	5.13319i	0.0697053	+	0.183798i
$781$	4.57493	+	52.8757i	0.163704	+	1.89204i
$782$	−7.43034	+	10.0074i	−0.265708	+	0.357863i
$783$	−45.6638	−	18.2256i	−1.63189	−	0.651331i
$784$	40.8764	+	36.2133i	1.45987	+	1.29333i
$785$	13.7271	+	2.88478i	0.489941	+	0.102962i
$786$	−1.76602	+	2.55852i	−0.0629918	+	0.0912593i
$787$	37.4098	−	35.5210i	1.33351	−	1.26619i	0.395995	−	0.918253i	$-0.370400\pi$
$787$	37.4098	−	35.5210i	1.33351	−	1.26619i	0.937519	−	0.347934i	$-0.113117\pi$
$788$	20.1905	−	2.09862i	0.719256	−	0.0747601i
$789$	1.59225	+	30.7202i	0.0566857	+	1.09367i
$790$	−2.60992	−	1.25687i	−0.0928569	−	0.0447175i
$791$	72.6179	+	31.9319i	2.58200	+	1.13537i
$792$	19.3776	−	4.77614i	0.688552	−	0.169713i
$793$	−3.28223	+	3.11652i	−0.116555	+	0.110671i
$794$	−5.30652	−	1.90840i	−0.188321	−	0.0677264i
$795$	−18.9888	+	7.57892i	−0.673463	+	0.268797i
$796$	6.36429	−	24.0282i	0.225576	−	0.851656i
$797$	10.8917	+	23.6527i	0.385804	+	0.837823i	0.998858	+	0.0477825i	$0.0152154\pi$
$797$	10.8917	+	23.6527i	0.385804	+	0.837823i	−0.613054	+	0.790041i	$0.710059\pi$
$798$	2.38429	−	19.6364i	0.0844029	−	0.695120i
$799$	4.12602	+	47.6873i	0.145968	+	1.68705i
$800$	−14.8563	+	25.0613i	−0.525248	+	0.886051i
$801$	−18.1665	−	47.9011i	−0.641881	−	1.69250i
$802$	−55.2286	−	45.6249i	−1.95019	−	1.61107i
$803$	14.2880	−	31.0283i	0.504212	−	1.09496i
$804$	23.2866	+	14.3531i	0.821254	+	0.506195i
$805$	0.703036	−	3.65799i	0.0247788	−	0.128927i
$806$	−0.456301	+	26.4320i	−0.0160725	+	0.931026i
$807$	−6.28265	+	0.873140i	−0.221160	+	0.0307360i
$808$	4.31876	−	6.25681i	0.151933	−	0.220114i
$809$	10.7482	+	11.7183i	0.377887	+	0.411995i	0.896521	−	0.443002i	$-0.146087\pi$
$809$	10.7482	+	11.7183i	0.377887	+	0.411995i	−0.518634	+	0.854997i	$0.673559\pi$
$810$	−1.34279	−	0.234116i	−0.0471810	−	0.00822600i
$811$	−0.250458	−	14.5082i	−0.00879479	−	0.509452i	−0.971257	−	0.238035i	$-0.923497\pi$
$811$	−0.250458	−	14.5082i	−0.00879479	−	0.509452i	0.962462	−	0.271417i	$-0.0874923\pi$
$812$	9.13165	+	58.3062i	0.320458	+	2.04615i
$813$	−15.2110	−	5.47036i	−0.533472	−	0.191854i
$814$	−1.76633	+	0.245478i	−0.0619098	+	0.00860401i
$815$	7.25276	−	7.37905i	0.254053	−	0.258477i
$816$	6.33931	−	73.2678i	0.221920	−	2.56489i
$817$	−1.24629	+	2.97246i	−0.0436021	+	0.103993i
$818$	−7.40305	+	11.5592i	−0.258842	+	0.404158i
$819$	−41.2368	−	13.2414i	−1.44093	−	0.462693i
$820$	−2.51609	+	4.24444i	−0.0878658	+	0.148222i
$821$	−17.3808	+	29.3200i	−0.606594	+	1.02327i	0.388220	+	0.921567i	$0.373090\pi$
$821$	−17.3808	+	29.3200i	−0.606594	+	1.02327i	−0.994814	+	0.101708i	$0.967569\pi$
$822$	−105.068	−	33.7380i	−3.66466	−	1.17675i
$823$	−27.5356	+	42.9944i	−0.959831	+	1.49869i	−0.0957084	+	0.995409i	$0.530512\pi$
$823$	−27.5356	+	42.9944i	−0.959831	+	1.49869i	−0.864122	+	0.503282i	$0.832126\pi$
$824$	−0.764338	+	1.82298i	−0.0266270	+	0.0635067i
$825$	−3.70972	+	42.8759i	−0.129156	+	1.49275i
$826$	55.1193	−	56.0791i	1.91785	−	1.95124i
$827$	−11.9628	+	1.66254i	−0.415986	+	0.0578123i	−0.342577	−	0.939490i	$-0.611300\pi$
$827$	−11.9628	+	1.66254i	−0.415986	+	0.0578123i	−0.0734087	+	0.997302i	$0.523388\pi$
$828$	−7.35535	−	2.64522i	−0.255616	−	0.0919278i
$829$	−2.34368	−	14.9646i	−0.0813994	−	0.519740i	−0.993866	−	0.110590i	$-0.964726\pi$
$829$	−2.34368	−	14.9646i	−0.0813994	−	0.519740i	0.912467	−	0.409151i	$-0.134175\pi$
$830$	−0.209302	−	12.1242i	−0.00726499	−	0.420836i
$831$	18.0250	+	3.14266i	0.625281	+	0.109018i
$832$	2.85019	+	3.10744i	0.0988124	+	0.107731i
$833$	34.2963	−	49.6868i	1.18830	−	1.72155i
$834$	−39.1956	+	5.44726i	−1.35723	+	0.188623i
$835$	0.143108	−	8.28977i	0.00495246	−	0.286879i
$836$	−0.785708	+	4.08815i	−0.0271743	+	0.141392i
$837$	26.6793	+	16.4443i	0.922172	+	0.568397i
$838$	−4.22314	+	9.17111i	−0.145886	+	0.316811i
$839$	−3.93260	−	3.24876i	−0.135768	−	0.112160i	0.566534	−	0.824038i	$-0.308284\pi$
$839$	−3.93260	−	3.24876i	−0.135768	−	0.112160i	−0.702302	+	0.711879i	$0.747844\pi$
$840$	3.59442	+	9.47770i	0.124019	+	0.327012i
$841$	41.4191	−	69.8706i	1.42824	−	2.40933i
$842$	3.13119	+	36.1893i	0.107908	+	1.24717i
$843$	−0.388050	+	3.19588i	−0.0133652	+	0.110072i
$844$	5.57024	+	12.0965i	0.191735	+	0.416379i
$845$	−1.47055	+	5.55201i	−0.0505885	+	0.190995i
$846$	−70.1358	+	27.9931i	−2.41132	+	0.962421i
$847$	−3.14615	−	1.13146i	−0.108103	−	0.0388773i
$848$	−37.8423	+	35.9317i	−1.29951	+	1.23390i
$849$	34.5129	−	8.50667i	1.18448	−	0.291948i
$850$	40.8299	+	17.9539i	1.40045	+	0.615814i
$851$	−0.324550	−	0.156295i	−0.0111254	−	0.00535772i
$852$	2.92789	+	56.4893i	0.100308	+	1.93529i
$853$	−40.1884	+	4.17722i	−1.37603	+	0.143025i	−0.762673	−	0.646784i	$-0.776114\pi$
$853$	−40.1884	+	4.17722i	−1.37603	+	0.143025i	−0.613353	+	0.789809i	$0.710180\pi$
$854$	11.7503	−	11.1570i	0.402086	−	0.381785i
$855$	1.69414	−	2.45438i	0.0579383	−	0.0839381i
$856$	1.01258	+	0.212796i	0.0346093	+	0.00727323i
$857$	7.16498	+	6.34762i	0.244751	+	0.216831i	0.776576	−	0.630024i	$-0.216955\pi$
$857$	7.16498	+	6.34762i	0.244751	+	0.216831i	−0.531825	+	0.846855i	$0.678493\pi$
$858$	34.9237	+	13.9390i	1.19228	+	0.475868i
$859$	11.0928	−	14.9400i	0.378481	−	0.509747i	−0.572117	−	0.820172i	$-0.693878\pi$
$859$	11.0928	−	14.9400i	0.378481	−	0.509747i	0.950598	+	0.310424i	$0.100471\pi$
$860$	0.276056	+	3.19057i	0.00941344	+	0.108798i
$861$	−22.6349	−	59.6833i	−0.771396	−	2.03400i
$862$	47.3232	−	29.1685i	1.61184	−	0.993484i
$863$	4.04075	+	33.2786i	0.137549	+	1.13282i	0.884037	+	0.467417i	$0.154815\pi$
$863$	4.04075	+	33.2786i	0.137549	+	1.13282i	−0.746488	+	0.665399i	$0.768262\pi$
$864$	29.5328	−	6.20638i	1.00473	−	0.211145i
$865$	−3.95876	−	2.83466i	−0.134602	−	0.0963812i
$866$	−25.8074	+	7.31453i	−0.876973	+	0.248558i
$867$	−34.1440	+	1.17922i	−1.15959	+	0.0400485i
$868$	0.649326	−	37.6133i	0.0220395	−	1.27668i
$869$	−7.32492	+	2.92357i	−0.248481	+	0.0991752i
$870$	−11.8241	+	34.7505i	−0.400874	+	1.17815i
$871$	−6.26792	−	14.9493i	−0.212380	−	0.506538i
$872$	8.58909	+	12.4435i	0.290863	+	0.421388i
$873$	34.4796	+	7.24597i	1.16696	+	0.245239i
$874$	−1.48293	+	1.50875i	−0.0501608	+	0.0510342i
$875$	−28.0545	+	0.968912i	−0.948417	+	0.0327552i
$876$	16.3604	−	32.5244i	0.552768	−	1.09890i
$877$	50.2350	−	26.3654i	1.69632	−	0.890295i	0.714700	−	0.699432i	$-0.246563\pi$
$877$	50.2350	−	26.3654i	1.69632	−	0.890295i	0.981617	−	0.190864i	$-0.0611289\pi$
$878$	−14.8392	−	17.3441i	−0.500798	−	0.585335i
$879$	−51.9468	+	34.5479i	−1.75212	+	1.16527i
$880$	−3.36584	−	11.1389i	−0.113462	−	0.375493i
$881$	−35.0793	+	21.6218i	−1.18185	+	0.728456i	−0.968620	−	0.248545i	$-0.920047\pi$
$881$	−35.0793	+	21.6218i	−1.18185	+	0.728456i	−0.213232	+	0.977002i	$0.568399\pi$
$882$	90.6894	+	29.1210i	3.05367	+	0.980556i
$883$	−15.9168	+	21.4371i	−0.535642	+	0.721416i	−0.985119	−	0.171876i	$-0.945017\pi$
$883$	−15.9168	+	21.4371i	−0.535642	+	0.721416i	0.449477	+	0.893292i	$0.351610\pi$
$884$	10.0708	−	11.7708i	0.338719	−	0.395896i
$885$	18.5095	−	5.94354i	0.622191	−	0.199790i
$886$	−14.8243	+	43.5681i	−0.498034	+	1.46370i
$887$	−1.03193	−	6.58894i	−0.0346488	−	0.221235i	0.964420	−	0.264374i	$-0.0851653\pi$
$887$	−1.03193	−	6.58894i	−0.0346488	−	0.221235i	−0.999069	+	0.0431389i	$0.986264\pi$
$888$	0.974997	−	0.101342i	0.0327187	−	0.00340082i
$889$	−17.0239	−	0.587949i	−0.570963	−	0.0197192i
$890$	−12.6110	+	5.54536i	−0.422722	+	0.185881i
$891$	−2.94091	+	2.26337i	−0.0985241	+	0.0758256i
$892$	−10.8714	−	1.12998i	−0.364002	−	0.0378347i
$893$	−0.420512	+	8.11315i	−0.0140719	+	0.271496i
$894$	26.9123	+	0.929463i	0.900082	+	0.0310859i
$895$	8.23137	−	2.02885i	0.275144	−	0.0678170i
$896$	26.9099	+	29.3388i	0.898997	+	0.980140i
$897$	4.31482	+	6.25109i	0.144068	+	0.208718i
$898$	−12.6605	+	55.4694i	−0.422488	+	1.85104i
$899$	−45.6763	+	53.3867i	−1.52339	+	1.78054i
$900$	−3.37157	+	27.7673i	−0.112386	+	0.925578i
$901$	44.4772	+	36.7430i	1.48175	+	1.22409i
$902$	9.77554	+	32.3512i	0.325490	+	1.07718i
$903$	−34.4968	−	22.9425i	−1.14798	−	0.763480i
$904$	20.0601	+	11.4283i	0.667190	+	0.380101i
$905$	8.83787	+	8.39166i	0.293781	+	0.278948i
$906$	25.6044	+	50.9013i	0.850649	+	1.69108i
$907$	20.4671	−	9.85642i	0.679598	−	0.327277i	−0.0620438	−	0.998073i	$-0.519762\pi$
$907$	20.4671	−	9.85642i	0.679598	−	0.327277i	0.741642	+	0.670796i	$0.234048\pi$
$908$	−5.90090	+	11.7310i	−0.195828	+	0.389306i
$909$	5.42643	−	28.2344i	0.179983	−	0.936477i
$910$	−2.98201	+	11.2585i	−0.0988527	+	0.373215i
$911$	5.78356	−	1.85714i	0.191618	−	0.0615299i	−0.208371	−	0.978050i	$-0.566816\pi$
$911$	5.78356	−	1.85714i	0.191618	−	0.0615299i	0.399989	+	0.916520i	$0.369014\pi$
$912$	2.77750	−	12.1690i	0.0919722	−	0.402956i
$913$	−24.7115	−	21.8924i	−0.817830	−	0.724534i
$914$	−0.529900	+	6.12443i	−0.0175275	+	0.202578i
$915$	3.85417	−	1.09238i	0.127415	−	0.0361129i
$916$	8.10199	−	3.90171i	0.267697	−	0.128916i
$917$	−2.46691	+	0.887180i	−0.0814645	+	0.0292973i
$918$	−14.8824	−	43.7388i	−0.491193	−	1.44360i
$919$	−45.5956	+	3.15320i	−1.50406	+	0.104015i	−0.797362	−	0.603501i	$-0.793772\pi$
$919$	−45.5956	+	3.15320i	−1.50406	+	0.104015i	−0.706697	+	0.707516i	$0.749816\pi$
$920$	0.313572	−	1.03774i	0.0103382	−	0.0342132i
$921$	−72.8085	−	48.4222i	−2.39912	−	1.59557i
$922$	−6.00711	−	49.4730i	−0.197834	−	1.62931i
$923$	18.0781	−	28.2273i	0.595046	−	0.929113i
$924$	−49.6972	−	19.8354i	−1.63492	−	0.652538i
$925$	−0.286840	+	1.25673i	−0.00943125	+	0.0413210i
$926$	−14.4601	−	34.4879i	−0.475187	−	1.13334i
$927$	0.129033	+	7.47443i	0.00423799	+	0.245492i
$928$	3.50189	+	67.5638i	0.114955	+	2.21789i
$929$	1.31467	−	25.3646i	0.0431329	−	0.832186i	−0.886281	−	0.463148i	$-0.846720\pi$
$929$	1.31467	−	25.3646i	0.0431329	−	0.832186i	0.929414	−	0.369039i	$-0.120313\pi$
$930$	11.2296	−	20.5271i	0.368232	−	0.673110i
$931$	6.92645	−	7.55162i	0.227005	−	0.247494i
$932$	27.2972	+	3.79367i	0.894149	+	0.124266i
$933$	3.16439	−	20.2049i	0.103598	−	0.661478i
$934$	−27.9063	+	51.0114i	−0.913123	+	1.66914i
$935$	−11.7763	+	5.17830i	−0.385125	+	0.169349i
$936$	−11.5385	−	5.07377i	−0.377148	−	0.165841i
$937$	−36.4587	−	6.35657i	−1.19105	−	0.207660i	−0.458704	−	0.888589i	$-0.651686\pi$
$937$	−36.4587	−	6.35657i	−1.19105	−	0.207660i	−0.732349	+	0.680929i	$0.761576\pi$
$938$	22.4389	+	53.5180i	0.732657	+	1.74742i
$939$	76.2415	−	24.4817i	2.48805	−	0.798930i
$940$	3.37624	+	7.33196i	0.110121	+	0.239142i
$941$	−11.5351	+	25.0500i	−0.376033	+	0.816606i	0.623365	+	0.781931i	$0.285765\pi$
$941$	−11.5351	+	25.0500i	−0.376033	+	0.816606i	−0.999399	+	0.0346752i	$0.988960\pi$
$942$	85.2625	−	56.7049i	2.77800	−	1.84754i
$943$	−1.97464	+	6.53487i	−0.0643030	+	0.212805i
$944$	38.2535	−	31.6016i	1.24505	−	1.02854i
$945$	9.67860	+	9.84713i	0.314845	+	0.320327i
$946$	17.3830	+	13.3782i	0.565171	+	0.434964i
$947$	−7.46569	−	13.6469i	−0.242602	−	0.443465i	0.727518	−	0.686088i	$-0.240674\pi$
$947$	−7.46569	−	13.6469i	−0.242602	−	0.443465i	−0.970121	+	0.242623i	$0.921992\pi$
$948$	−7.90976	+	2.84460i	−0.256897	+	0.0923885i
$949$	−19.1035	+	10.0263i	−0.620126	+	0.325467i
$950$	6.44449	+	3.97217i	0.209087	+	0.128874i
$951$	−17.9294	−	38.9360i	−0.581400	−	1.26259i
$952$	18.5943	−	21.7332i	0.602646	−	0.704376i
$953$	0.542152	+	0.216387i	0.0175620	+	0.00700947i	0.379455	−	0.925210i	$-0.376111\pi$
$953$	0.542152	+	0.216387i	0.0175620	+	0.00700947i	−0.361893	+	0.932219i	$0.617870\pi$
$954$	−35.1935	+	83.9382i	−1.13943	+	2.71760i
$955$	−6.19050	−	4.43268i	−0.200320	−	0.143438i
$956$	−3.48955	−	6.93721i	−0.112860	−	0.224365i
$957$	47.9641	+	87.6761i	1.55046	+	2.83417i
$958$	−53.9734	+	47.8162i	−1.74380	+	1.54487i
$959$	−55.4740	−	74.7138i	−1.79135	−	2.41263i
$960$	−0.955549	−	3.60764i	−0.0308402	−	0.116436i
$961$	10.6279	−	8.77983i	0.342836	−	0.283220i
$962$	0.978631	+	0.557530i	0.0315523	+	0.0179755i
$963$	3.82934	−	0.804744i	0.123399	−	0.0259325i
$964$	4.72650	−	11.2729i	0.152230	−	0.363077i
$965$	6.02516	+	5.33782i	0.193957	+	0.171831i
$966$	−15.4469	−	22.3787i	−0.496996	−	0.720022i
$967$	−34.3386	−	5.98694i	−1.10425	−	0.192527i	−0.409879	−	0.912140i	$-0.634429\pi$
$967$	−34.3386	−	5.98694i	−1.10425	−	0.192527i	−0.694376	+	0.719613i	$0.744319\pi$
$968$	−0.876681	−	0.422187i	−0.0281776	−	0.0135696i
$969$	−13.7254	−	1.42663i	−0.440924	−	0.0458300i
$970$	1.46598	−	9.36038i	0.0470698	−	0.300544i
$971$	−7.95888	−	34.8701i	−0.255413	−	1.11904i	−0.926095	−	0.377291i	$-0.876856\pi$
$971$	−7.95888	−	34.8701i	−0.255413	−	1.11904i	0.670682	−	0.741745i	$-0.266001\pi$
$972$	−18.2880	+	13.0950i	−0.586587	+	0.420023i
$973$	−29.5478	−	15.5079i	−0.947260	−	0.497160i
$974$	2.45787	+	10.7686i	0.0787553	+	0.345049i
$975$	18.3727	−	20.0310i	0.588397	−	0.641505i
$976$	8.10279	−	6.23602i	0.259364	−	0.199610i
$977$	11.8017	+	5.68338i	0.377569	+	0.181828i	0.613036	−	0.790055i	$-0.289948\pi$
$977$	11.8017	+	5.68338i	0.377569	+	0.181828i	−0.235468	+	0.971882i	$0.575662\pi$
$978$	−1.30371	−	75.5194i	−0.0416880	−	2.41484i
$979$	−12.0819	+	35.5083i	−0.386140	+	1.13485i
$980$	2.60683	−	9.84201i	0.0832723	−	0.314392i
$981$	48.6764	+	30.0026i	1.55412	+	0.957908i
$982$	−5.45947	−	6.38106i	−0.174219	−	0.203628i
$983$	30.9468	−	2.14015i	0.987048	−	0.0682602i	0.433567	−	0.901122i	$-0.357255\pi$
$983$	30.9468	−	2.14015i	0.987048	−	0.0682602i	0.553482	+	0.832861i	$0.313299\pi$
$984$	−4.75643	−	17.9577i	−0.151630	−	0.572472i
$985$	5.74204	+	8.96569i	0.182957	+	0.285671i
$986$	102.038	−	17.7903i	3.24954	−	0.566558i
$987$	−101.389	−	24.9902i	−3.22726	−	0.795448i
$988$	1.96802	−	1.74352i	0.0626112	−	0.0554687i
$989$	1.42726	+	4.19466i	0.0453842	+	0.133382i
$990$	−13.1944	−	15.4217i	−0.419347	−	0.490135i
$991$	13.8908	−	30.1656i	0.441254	−	0.958242i	−0.551056	−	0.834468i	$-0.685775\pi$
$991$	13.8908	−	30.1656i	0.441254	−	0.958242i	0.992310	−	0.123774i	$-0.0394998\pi$
$992$	5.19810	−	42.8102i	0.165040	−	1.35923i
$993$	−2.54465	+	3.42720i	−0.0807520	+	0.108759i
$994$	−64.7188	+	101.053i	−2.05275	+	3.20520i
$995$	12.7585	−	2.68123i	0.404471	−	0.0850006i
$996$	−25.5163	−	24.2280i	−0.808515	−	0.767694i
$997$	−43.6915	−	33.6257i	−1.38373	−	1.06494i	−0.989282	−	0.146015i	$-0.953355\pi$
$997$	−43.6915	−	33.6257i	−1.38373	−	1.06494i	−0.394443	−	0.918920i	$-0.629062\pi$
$998$	19.9699	+	4.92215i	0.632138	+	0.155808i
$999$	1.16018	−	0.660958i	0.0367064	−	0.0209118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.m.a.10.9	✓	3168
547.383	even	91	inner	547.2.m.a.383.9	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.m.a.10.9	✓	3168	1.1	even	1	trivial
547.2.m.a.383.9	yes	3168	547.383	even	91	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.m (of order \(91\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.929069 - 1.56726i) q^{2} +(-0.617025 - 2.70336i) q^{3} +(-0.633268 + 1.15758i) q^{4} +(-0.691646 - 0.0238872i) q^{5} +(-3.66362 + 3.47865i) q^{6} +(-4.21969 + 0.586437i) q^{7} +(-1.23913 + 0.0427955i) q^{8} +(-4.22454 + 2.03443i) q^{9} +O(q^{10})\)	\(q+(-0.929069 - 1.56726i) q^{2} +(-0.617025 - 2.70336i) q^{3} +(-0.633268 + 1.15758i) q^{4} +(-0.691646 - 0.0238872i) q^{5} +(-3.66362 + 3.47865i) q^{6} +(-4.21969 + 0.586437i) q^{7} +(-1.23913 + 0.0427955i) q^{8} +(-4.22454 + 2.03443i) q^{9} +(0.605149 + 1.10618i) q^{10} +(3.33315 + 0.821546i) q^{11} +(3.52011 + 0.997695i) q^{12} +(-1.35182 - 1.69513i) q^{13} +(4.83948 + 6.06851i) q^{14} +(0.362187 + 1.88451i) q^{15} +(2.64155 + 4.12455i) q^{16} +(4.17462 - 3.44869i) q^{17} +(7.11337 + 4.73084i) q^{18} +(0.782372 - 0.482229i) q^{19} +(0.465649 - 0.785512i) q^{20} +(4.18900 + 11.0455i) q^{21} +(-1.80914 - 5.98719i) q^{22} +(0.365442 - 1.20940i) q^{23} +(0.880265 + 3.32341i) q^{24} +(-4.51028 - 0.311913i) q^{25} +(-1.40078 + 3.69356i) q^{26} +(2.91985 + 3.66138i) q^{27} +(1.99334 - 5.25601i) q^{28} +(-9.12227 + 5.19699i) q^{29} +(2.61702 - 2.31848i) q^{30} +(6.29734 - 2.26473i) q^{31} +(2.89575 - 5.75674i) q^{32} +(0.164305 - 9.51761i) q^{33} +(-9.28351 - 3.33865i) q^{34} +(2.93254 - 0.304811i) q^{35} +(0.320242 - 6.17860i) q^{36} +(0.0441166 - 0.281687i) q^{37} +(-1.48266 - 0.778159i) q^{38} +(-3.74845 + 4.70041i) q^{39} +0.858061 q^{40} -5.40341 q^{41} +(13.4193 - 16.8273i) q^{42} +(-2.85143 + 2.04176i) q^{43} +(-3.06178 + 3.33814i) q^{44} +(2.97048 - 1.30619i) q^{45} +(-2.23496 + 0.550869i) q^{46} +(-5.02148 + 7.27486i) q^{47} +(9.52025 - 9.68602i) q^{48} +(10.7271 - 3.04036i) q^{49} +(3.70151 + 7.35859i) q^{50} +(-11.8989 - 9.15757i) q^{51} +(2.81833 - 0.491375i) q^{52} +(2.01085 + 10.4627i) q^{53} +(3.02560 - 7.97785i) q^{54} +(-2.28573 - 0.647839i) q^{55} +(5.20364 - 0.907255i) q^{56} +(-1.78638 - 1.81749i) q^{57} +(16.6203 + 9.46863i) q^{58} +(-1.22110 - 10.0566i) q^{59} +(-2.41084 - 0.774138i) q^{60} +(-0.179947 - 2.07977i) q^{61} +(-9.40008 - 7.76549i) q^{62} +(16.6332 - 11.0621i) q^{63} +(-1.94015 + 0.134173i) q^{64} +(0.894492 + 1.20472i) q^{65} +(-15.0692 + 8.58501i) q^{66} +(7.19313 + 2.03873i) q^{67} +(1.34850 + 7.01642i) q^{68} +(-3.49493 - 0.241695i) q^{69} +(-3.20225 - 4.31287i) q^{70} +(4.98004 + 14.6361i) q^{71} +(5.14768 - 2.70171i) q^{72} +(1.87808 - 9.77191i) q^{73} +(-0.482466 + 0.192565i) q^{74} +(1.93974 + 12.3854i) q^{75} +(0.0627693 + 1.21104i) q^{76} +(-14.5466 - 1.51199i) q^{77} +(10.8493 + 1.50780i) q^{78} +(-1.86793 + 1.33752i) q^{79} +(-1.72850 - 2.91583i) q^{80} +(-0.674005 + 0.845176i) q^{81} +(5.02014 + 8.46857i) q^{82} +(-8.51542 - 4.46924i) q^{83} +(-15.4388 - 2.14564i) q^{84} +(-2.96974 + 2.28555i) q^{85} +(5.84914 + 2.57201i) q^{86} +(19.6780 + 21.4541i) q^{87} +(-4.16536 - 0.875359i) q^{88} +(-0.941816 + 10.8852i) q^{89} +(-4.80693 - 3.44198i) q^{90} +(6.69836 + 6.36017i) q^{91} +(1.16856 + 1.18890i) q^{92} +(-10.0080 - 15.6266i) q^{93} +(16.0669 + 1.11112i) q^{94} +(-0.552644 + 0.314843i) q^{95} +(-17.3493 - 4.27622i) q^{96} +(-5.95476 - 4.58287i) q^{97} +(-14.7313 - 13.9875i) q^{98} +(-15.7524 + 3.31040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Introduction

L-functions

Modular forms

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Database

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